Physics Archive: Questions from 2024-07-5

A cube of mass m = 0.45 kg is set against a spring with a spring constant of k1 = 591 N/m which has been compressed by a distance of 0.1 m. Some distance in front of it, along a frictionless surface, is another spring with a spring constant of k2 = 385 N/m. The cube is not connected to the first spring and may slide freely. Part (a) How far d2, in meters, will the second spring compress when the cube runs into it? Part (b) How fast v, in meters per second, will the cube be moving when it strikes the second spring? Part (c) Now assume friction is present on the surface in between the ends of the springs at their equilibrium lengths, and the coefficient of kinetic friction is μk = 0.5. If the distance between the springs is x = 1 m, how far d2, in meters, will the second spring now compress? d2 =

When the 150−lb skier is at point A he has a speed of 5 ft/s. Determine his speed when he reaches point B on the smooth slope. For this distance the slope follows the cosine curve shown. Also, what is the normal force on his skis at B and his rate of increase in speed? Neglect friction and air resistance.

In the figure, a 3.7 kg block is accelerated from rest by a compressed spring of spring constant 640 N/m. The block leaves the spring at the spring's relaxed length and then travels over a horizontal floor with a coefficient of kinetic friction μk = 0.231. The frictional force stops the block in distance D = 8.3 m. What are (a) the increase in the thermal energy of the block-floor system, (b) the maximum kinetic energy of the block, and (c) the original compression distance of the spring? (a) Number Units (b) Number Units (c) Number Units

A 4.50 kg block is pushed along a floor by a constant applied force that is horizontal and has a magnitude of 42.0 N. The figure gives the block's speed v versus time t as the block moves along an x-axis on the floor. The scale of the figure's vertical axis is set by vs = 5.20 m/s. What is the coefficient of kinetic friction between the block and the floor? Number Units

Two people (Moe and Sara) each slide an identical wooden box of books across the same rough level surface, as shown in the figure. In both cases the magnitude of the force (F) anc the angle (θ) are the same. Which statement is TRUE? a) The force of friction for Moe is less than the force of friction for Sara. b) The force of friction for Moe is equal to the force of friction for Sara. c) The force of friction for Moe is greater than the force of friction for Sara. d) The force of friction is impossible to determine.

A 46.3-kg box is being pushed a distance of 8.35 m across the floor by a force P whose magnitude is 170 N. The force P is parallel to the displacement of the box. The coefficient of kinetic friction is 0.227 . Determine the work done on the box by (a) the applied force, (b) the friction force, (c) the normal force, and (d) by the force of gravity. Be sure to include the proper plus or minus sign for the work done by each force. (a) Number Units (b) Number Units (c) Number Units (d) Number Units

Water from a fire hose is directed toward a building as shown in the figure below. The water leaves the hose at a speed of vi = 40.0 m/s and at an angle of θi = 40.0∘ above the horizontal. The base of the hose (at ground level) is a horizontal distance d = 61.0 m away from the building. Find the height h (in m) where the water strikes the building.

Consider the figure below. (a) Find the tension in each cable supporting the 572−N cat burglar. (Assume the angle θ of the inclined cable is 38.0∘.) inclined cable N horizontal cable N vertical cable N (b) Suppose the horizontal cable were reattached higher up on the wall. Would the tension in the inclined cable increase, decrease, or stay the same? increase decrease stay the same

A 6 Kg block has an initial velocity 5 m/s up a 30 degree incline. When the block has moved 1.25 m up the incline it has a the velocity, 2.8 m/s up the incline. There is friction. Calculate the magnitude of the work done by friction acting on the block as the block moves 1.25 m up the incline.

At time t, r→ = 4.20t2 i^ − (2.30t + 4.20t2)j^ gives the position of a 3.0 kg particle relative to the origin of an xy coordinate system ( r→ is in meters and t is in seconds). (a) Find the torque acting on the particle relative to the origin at the moment 6.41 s (b) Is the magnitude of the particle's angular momentum relative to the origin increasing, decreasing, or unchanging? (a) k^ Units (b)

A physics professor is pushed up a ramp inclined upward at an angle 29.0∘ above the horizontal as he sits in his desk chair that slides on frictionless rollers. The combined mass of the professor and chair is 80.0 kg. He is pushed a distance 2.40 m along the incline by a group of students who together exert a constant horizontal force of 610 N. The professor's speed at the bottom of the ramp is 2.15 m/s. Part A Use the work-energy theorem to find his speed at the top of the ramp. Express your answer in meters per second. v = m/s

Field and force with three charges At a particular moment, one negative and two positive charges are located as shown in the figure. Your answers to each part of this problem should be vectors. It helps a great deal to make a diagram with arrows representing the various electric field contributions, and then check the signs of your components against these arrows. Let Q1 = 1 μC, Q2 = 7 μC, and Q3 = −5 μC. (a) Find the electric field at the location of Q1, due to Q2 and Q3. E→ = N/C (b) Use the electric field you calculated in part (a) to find the force on Q1. F→ = N (c) Find the electric field at location A, due to all three charges. E→ = N/C (d) An alpha particle (He2+, containing two protons and two neutrons) is released from rest at location A. Use your answer from part (c) to determine the initial acceleration of the alpha particle. (Use 6.646×10−27 kg for the mass of He2+.) a→ = m/s2

A mass spectrometer can be used to measure the mass of an ion. An ion of mass m and charge q is produced, approximately at rest, in source S, a chamber in which a gas discharge is taking place. The ion is accelerated by the potential difference V and allowed to enter the magnetic field B. In the field, it moves in a semicircle and strikes a photographic plate at a distance x from the entry point. a) Show that the mass of the ion is; m = (B2qx2)/(8ΔV). b) Assume that; B = 125 mT V = 1500 v q = +3.2044 E−19 C m = 244.064200 u and find the location where the ion strikes the photographic plate.

Two children stand on the ground on opposite sides of a merry-go-round and try to rotate it by pushing in opposite directions with forces of magnitude 10.0 N (as shown when viewed from above). The merry-go-round has a mass of 180 kg and a radius of 2.0 m.

Ropes 3 m and 5 m in length are fastened to a holiday decoration that is suspended over a town square. The decoration has a mass of 7 kg. The ropes, fastened at different heights, make angles of 52∘ and 40∘ with the horizontal. Find the tension in each wire and the magnitude of each tension (in N). (Use g = 9.8 m/s2 for the acceleration due to gravity. Round your answers to two decimal places.)

In the arrangement shown below, an object can be hung from a string (with linear mass density μ = 0.00200 kg/m) that passes over a light pulley. The string is connected to a vibrator (of constant frequency f), and the length of the string between point P and the pulley is L = 1.50 m. When the mass m of the object is either 25.0 kg or 36.0 kg, standing waves are observed; no standing waves are observed with any mass between these values, however. m (a) What is the frequency of the vibrator (in Hz )? (Note: The greater the tension in the string, the smaller the number of nodes in the standing wave.) Hz (b) What is the largest object mass (in kg ) for which standing waves could be observed? kg (c) What If? What would the linear mass density of the string have to be (in kg/m) if 36.0 kg is the largest mass for which standing waves are observed? kg/m (d) For what values of m (in kg) would standing waves with the next four higher numbers of nodes be observed in this case? m2 = kgm3 = kg m4 = kg m5 = kg

J. J. Thomson is best known for his discoveries about the nature of cathode rays. His other important contribution was the invention, together with one of his students, of the mass spectrometer, a device that measures the ratio of mass m to (positive) charge q of an ion. The spectrometer consists of two regions as shown in the figure. (Figure 1) In the first region an electric field accelerates the ion and in the second the ion follows a circular arc in a magnetic field. The radius of curvature of the arc can be measured and then the m/q ratio can be found. Figure 1 of 1 After being accelerated to a speed of 1.69×105 m/s, the particle enters a uniform magnetic field of strength 0.900 T and travels in a circle of radius 35.0 cm (determined by observing where it hits the screen as shown in the figure). The results of this experiment allow one to find m/q. Find the ratio m/q for this particle. Express your answer numerically in kilograms per coulomb. View Available Hint(s)

The drawing shows three point charges fixed in place. The charge at the coordinate origin has a value of q1 = +7.89 μC; the other two have identical magnitudes, but opposite signs: q2 = −5.15 μC and q3 = +5.15 μ C. (a) Determine the net force exerted on q1 by the other two charges. (b) If q1 had a mass of 1.50 g and it were free to move, what would be its acceleration?

The figure shows a cord attached to a cart that can slide along a frictionless horizontal rail aligned along an x axis. The left end of the cord is pulled over a pulley, of negligible mass and friction and at cord height h = 1.6 m, so the cart slides from x1 = 5.0 m to x2 = 1.0 m. During the move, the tension in the cord is a constant 27.0 N. What is the change in the kinetic energy of the cart during the move? Number Units

A man on a motorcycle plans to make a jump as shown in the figure. If he leaves the ramp with a speed of 37.5 m/s and has a speed of 35.0 m/s at the top of his trajectory, determine his maximum height (h) (in m) above the end of the ramp. Ignore friction and air resistance. m

Question 1: A small metal cylinder rests on a circular turntable that is rotating at a constant rate, as illustrated in the diagram. Which of the following sets of vectors best describes the velocity, acceleration, and net force acting on the cylinder at the point indicated in the diagram? a b d c

Question 2: Let R be the distance between the cylinder and the center of the turntable. Now assume that the cylinder is moved to a new location R/2 from the center of the turntable. Which of the following statements accurately describe the motion of the cylinder at the new location? Check all that apply. (a) The speed of the cylinder has decreased. (b) The speed of the cylinder has increased. (C) The magnitude of the acceleration of the cylinder has decreased. (d) The magnitude of the acceleration of the cylinder has increased. (E) The speed and the acceleration of the cylinder have not changed.

Hooks Law & Springs Question 1: 2 Springs are attached together in line with one side anchored as shown above. Both springs individually have a spring constant of 300 N/m. 100 Newtons were applied to the free end of the yellow spring and the end moved 0.667 m. What is the spring constant (in N/m) of the combined springs? Question 2: The bottom of Spring 1, in the picture above, started level with the blue dotted line. Once the 250 kg block was attached, the spring stretched, and the bottom is now at the dotted green line. Assume the acceleration due to gravity is 9.8 m/s2. What is the spring constant of Spring 1 in N/m? (Use the Following Units for the Calculations: Newtons, meters, kg, etc.) Question 3: The bottom of Spring 2, in the picture above, started level with the blue dotted line. Once the blue block was attached, the spring stretched, and the bottom is now at the dotted green line. Spring 2 has a spring constant of 3.5 N/m. Assume the acceleration due to gravity is 9.8 m/s2. What is the mass of the blue block in kilograms? (Use the Following Units for the Calculations: Newtons, meters, kg, etc.)

Two blocks of masses m1 = 5.0 kg and m2 = 6.0 kg are connected by a light string passes over a light frictionless pulley as shown in figure below. The mass m1 is at rest on the inclined plane and m2 hangs vertically. Find the magnitude and direction of the force of friction on the 5.0 kg block

A box of mass 4.00 kg is attached to a spring of force constant k = 350 N/m. The block is pulled to the right 35 cm away from the equilibrium point and released from rest. The block and spring are on a frictionless surface. a) What is the speed of the block at the equilibrium point? b) What is the frequency of the motion of the block? c) What is the acceleration of the block after 2 seconds?

Two cars with masses M1 and M2, initially moving with the speeds v1i and v2i, collide as shown. Video from a traffic camera measured v2i. The video also showed that immediately after the collision the two cars were moving with the same velocity, speed vf. You want to determine v1i or v2i. A) Draw diagrams showing the momenta of the cars. B) Write down the momentum conservation equations for the collision in x and y. C) Write down an equation that can be solved for v1i in terms of the masses and speeds defined in the question. D) What is v1i? (In some versions, v1i is given and you solve for v2i.)

A grinding wheel is in the form of a uniform solid disk of radius 7.06 cm and mass 2.02 kg. It starts from rest and accelerates uniformly under the action of the constant torque of 0.602 N-m that the motor exerts on the wheel. (a) How long does the wheel take to reach its final operating speed of 1180 rev/min? s (b) Through how many revolutions does it turn while accelerating? rev

A spring is used as a bumper to keep trucks from running into a loading dock. The spring has constant is k and is designed for a truck of mass M initially moving with speed vi. When the truck hits the bumper, the spring compresses the designed distance Δxd in stopping the truck. Assume friction can be neglected. There will be a problem with this design if the truck hits the bumper with a greater speed, vnew . You want to determine the speed of the truck, vf, when the spring is compressed the distance Δxd if the initial speed of the truck is vnew. A) Define the system and identify all the energies and all work. B) Write an energy equation that can be solved for the spring constant k. C) If vnew > vi write an energy equation that can be solved for the speed of the truck when the spring is compressed a distance Δx. D). What is vf of the truck when the spring is compressed the design distance, Δxd?

3.1 A force F→ = (6ı^ − 2ȷ^)N acts on a particle that undergoes a displacement Δr→ = (3ı^ + ȷ^)m. 3.1.1 Find the work done by force on the particle. 3.1.2 The angle between F→ and Δr→. 3.2 The force acting on a particle is Fx = (8x − 16)N, where x is in meters. Find the net work done by this force on a particle as it moves from x = 0 to x = 3.00 3.3 A grasshopper launches itself at an angle of 45∘ from the ground and rises to a maximum height of 1.0 m above the ground. Ignoring the effects of air friction, use conservation of mechanical energy to calculate its initial speed.

A man on a motorcycle plans to make a jump as shown in the figure. If he leaves the ramp with a speed of 35.5 m/s and has a speed of 33.0 m/s at the top of his trajectory, determine his maximum height (h) (in m) above the end of the ramp. Ignore friction and air resistance. m

Two forces, F→1 and F→2, act on the 7.00−kg block shown in the drawing. The magnitudes of the forces are F1 = 68.0 N and F2 = 28.3 N. Take the positive direction to be to the right. Find the horizontal acceleration of the block, including sign. Number Units

The professor holds the 5.0 kg bowling ball at rest in front of her face, a height of 1.70 m above the ground. She releases the ball (being careful not to impart any initial velocity or move her head). a) If the system were frictionless, find the speed of the ball at its lowest point, 0.50 m above the ground. b) If the system were frictionless, find the height of the ball at its next close approach to the professor's face. c) If the ball only reaches a height of 1.69 m at its next close approach to the professor's face, find the work done by friction during one period of the pendulum's motion.

A cable is lifting a construction worker and a crate, as the drawing shows. The weights of the worker and crate are 833 N and 1660 N, respectively. The acceleration of the cable is 0.620 m/s2, upward. What is the tension in the cable (a) below the worker and (b) above the worker? (a) Number Units (b) Number Units

Learning Goal: A car of weight 3450 lb is traveling around a curve of constant curvature ρ (Figure 1) Figure 1 of 1 Part A - Finding the net friction force The car is traveling at a speed of 74.5 ft/s, which is increasing at a rate of 4.55 ft/s2. and the curvature of the road is ρ = 630 ft. What is the magnitude of the net frictional force that the road exerts on the tires? Express your answer to three significant figures and include the appropriate units. View Available Hint(s) F = Value Units Units ? Part B - Finding the maximum allowable acceleration Suppose that the tires are capable of exerting a maximum friction force of 2350 lb. If the car is traveling at 73.5 ft/s and the curvature of the road is ρ = 450 ft what is the maximum tangential acceleration that the car can have without sliding? Express your answer to three significant figures and include the appropriate units. View Available Hint(s) amax = Value Units Units Part C - Finding the minimum curvature of the road Suppose that the tires are capable of exerting a maximum net friction force of 755 lb. If the car is traveling at 70.5 ft/s, what is the minimum curvature of the road that will allow the car to accelerate at 3.65 ft/s2 without sliding? Express your answer to three significant figures and include the appropriate units. View Available Hint(s) ρmin = Value Units

During a hammer thrower's practice swing, the 5 kg head of the hammer revolves at a constant speed in a horizontal circle as shown. Knowing that the speed of the hammer is 3 m/sec and θ = 45∘ (a) draw free body diagram of the forces acting on the hammer (5 points) (b) the tension in wire BC ( 10 points) (c) the radius of the circle (10 points) Fig. P12.37

A box slides from rest down a frictionless ramp inclined at 31.0∘ with respect to the horizontal and is stopped at the bottom of the ramp by a spring with a spring constant of k = 3.00×104 N/m. If the box has a mass of 12.0 kg and slides 3.00 m from the point of release to the point where it comes to rest against the spring, determine the compression (in m ) of the spring when the box comes to rest.

A concave mirror (f = 63 cm) produces an image whose distance from the mirror is one-third the object distance. Determine (a) the object distance and (b) the (positive) image distance. (a) Number Units (b) Number Units

A point charge q = +39.0 μC moves from A to B separated by a distance d = 0.184 m in the presence of an external electric field E→ of magnitude 255 N/C directed toward the right as in the following figure. (a) Find the electric force exerted on the charge. magnitude N direction (b) Find the work done by the electric force. J (c) Find the change in the electric potential energy of the charge. J (d) Find the potential difference between A and B. vB−vA = V

The following is a graph of an object's velocity over time. a) What is the total displacement of the object between t = 0.0 s and t = 2.0 s? b) At what times, if any, does the golf cart change directions? How can you tell? c) What is the maximum displacement the object reaches from its starting point? At what time does it reach this displacement? d) Draw an acceleration vs time graph for the object over the same time interval. Include numbers and labels on your axes.

An object is moving in the xy-plane along the path shown by the blue curve. The object moves at constant speed. Which of the diagrams shown below shows the velocity vectors of the object at the points P1 and P2? 2 1 3 4

In the figure particle 1 of charge q1 = 1.05 μC and particle 2 of charge q2 = −3.07 μC, are held at separation L = 10.7 cm on an x axis. If particle 3 of unknown charge q3 is to be located such that the net electrostatic force on it from particles 1 and 2 is zero, what must be the (a) x and (b) y coordinates of particle 3?

For the system of capacitors shown in the figure below, find the following. (Let C1 = 1.00 μF and C2 = 6.00 μF.) (a) the equivalent capacitance of the system μF (b) the charge on each capacitor on C1 μC on C2 μC on the 6.00 μF capacitor μC on the 2.00 μF capacitor μC (c) the potential difference across each capacitor across C1 V across C2 V across the 6.00 μF capacitor V across the 2.00 μF capacitor V

The equipotential lines in a region of electric field are shown in the diagram below. For each path indicated below, what is the work done by the electric field in moving a charge q = +1.4×10−7 C along that path? Here V0 = +150 V. (a) from A to B WAB = J (b) from A to C WAC = J (c) from A to D WAD = J (d) from D to C WDC = J

Two point charges are enclosed by a spherical conducting shell that has an inner and outer radius of 13.0 cm and 15.2 cm, respectively. One point charge has a charge of q1 = 9.30 μC, while the second point charge has an unknown charge q2. The conducting shell is known to have a net electric charge of −3.10 μC, but measurements find that the charge on the outer surface of the shell is 3.70 μC. Determine the charge q2 of the second point charge in units of microcoulombs. q2 = μC TOOLS ×10y

What is the ratio of potential energy of the charge systems drawn below (U2/U1)? All charges are equal in magnitude except the upper two charges on the right are halved. (1 A = 1 Angstrom = 10−10 m)

In the figure, there are two equal point charges, with charge Q = −10.1μC (microCoulombs). One is at x = 0 and the other is at x2 = 0.51 m. How much work must be done on the system of the two charges to move the right charge from its initial position to the point x = 0.098 m? The charge starts and ends a rest (velocity equal to zero). Give your answer in Joules to at least three significant figures to avoid being counted off due to rounding. Do not include units in your answer. A microCoulomb is 10−6 Coulombs

A bar with a length of L = 0.50 m slide without friction on horizontal rails, as shown in Figure 1. There is a uniform magnetic field of B = 2.0 T directed into the plane. At one end of the rails, there is a battery with an emf of ε = 15 V and a switch. The bar has a mass of 0.90 kg and a resistance of 5.0 Ω, while any other resistance in the circuit is negligible. The switch is closed at t = 0. Figure 1 (a) Plot the speed of the bar as a function of time. (b) What is the acceleration of the bar immediately after the switch is closed? (c) What is the acceleration of the bar when its speed reaches 2.0 m/s? (d) What is the terminal speed of the bar?

A person with mass 55.0 kg stands 2.00 m away from the wall on a uniform 6.00−m beam, as shown in the figure. The mass of the beam is 40.0 kg. a) Draw a free-body diagram of the beam, similar to Figure 8.18 b. There are four forces that act on the beam. Give each force a subscript letter. b) Write an expression for Στi, the net torque on the beam around the pin on its left end, similar to the first equation on p. 238. c) For each of the four forces on the beam, what is the angle θ between the force and the position vector? (The position vector goes from the pin to where the force is applied to the beam. Also, if the position vector is zero any of the forces, give τ = 0 as your answer.) d) For each force, the torque from that force is defined as τ = r→×F→ = rFsin⁡θ. Using this definition, evaluate your answer to part b), to write an equation similar to the 2 nd equation on p. 238. e) Solve the last equation for the tension in the cable.

The drawing shows a collision between two pucks on an air-hockey table. Puck A has a mass of 0.0350 kg and is moving along the x axis with a velocity of +4.88 m/s. It makes a collision with puck B, which has a mass of 0.0700 kg and is initially at rest. The collision is not head-on. After the collision, the two pucks fly apart with the angles shown in the drawing. Find the speed of (a) puck A and (b) puck B.

Mary applies a force of 71 N to push a box with an acceleration of 0.54 m/s2. When she increases the pushing force to 79 N, the box's acceleration changes to 0.79 m/s2. There is a constant friction force present between the floor and the box. (a) What is the mass of the box in kilograms? kg (b) What is the coefficient of kinetic friction between the floor and the box?

A man drags a 71-kg crate across the floor at a constant velocity by pulling on a strap attached to the bottom of the crate. The crate is tilted 25∘ above the horizontal, and the strap is inclined 61∘ above the horizontal. The center of gravity of the crate coincides with its geomentrical center, as indicated in the figure. Find the magnitude of the tension in the strap.

A ballistic (m = 500 g) is traveling with a speed v0 = 5 m/s directly towards the middle of a thin rod⁡(M = 2 kg, L = 2 m), as shown below. The ballistic collides with and sticks to the rod, causing it to swing about a hinge at an angle ϕ, as shown below. The moment of inertia of a rod rotating about one of its ends is Irod = 13 ML2. Part (a) Which of the following quantities are conserved during the collision? (4 points) (a) Mechanical Energy (b) Linear Momentum (c) Angular Momentum (d) Net Force Part (b) Find the angular speed of the ballistic-rod system after the collision. (8 points) Part (c) Determine the maximum angle to which the ballistic and rod swing after the collision. (8 points) Part (d) If you wanted the ballistic and rod to swing higher, should you aim the ballistic higher or lower? Defend your reasoning with a conceptual argument. (5 points)

Two titanium spheres approach each other head-on with the same speed and collide elastically. After the collision, one of the spheres, whose mass is 190 g, remains at rest. (a) What is the mass of the other sphere? (b) What is the speed of the two-sphere center of mass if the initial speed of each sphere is 3.5 m/s? (a) Number Units (b) Number Units

Two balls of identical mass of 2.166 kg and with identical charges placed on them hang from the ceiling on identical strings of lengths 0.710 m as shown. If the angle with respect to the vertical that the strings form is 27.5 degrees, what is the charge on each ball? Please give your answer in microcoulomb (i.e. do not enter a unit, but calculate your answer in micro-coulomb).

An initially uncharged 4.95 μF capacitor and a 7.17 kΩ resistor are connected in series at time t = 0 to a 1.50 V battery that has negligible internal resistance. What is the initial current I0 in the circuit in milliamperes? I0 = mA Calculate the circuit's time constant τ in milliseconds. τ = ms How much time t, in milliseconds, must elapse from the closing of the circuit for the current to decrease to 2.29% of its initial value? t = ms

A 1 mF, a 2 mF, and a 3 mF capacitor are connected in parallel, the combination being connected across a 9 volt battery. The capacitor with the greatest charge on it is the 1 mF the 2 mF the 3 mF neither since they all have the same charge

Mariana finds a cave to explore. Starting at the cave entrance, Mariana first follows a passage 75.0 m north, then turns and moves 250 m east, then goes 106 m at an angle 30.0∘ north of east, and finally moves 186 m south. Find the resultant displacement from the cave entrance. Shown is a sketch of the situation not drawn to scale. (Give the magnitude of the displacement in m and the direction in degrees south of east.) What is the resultant displacement from the entrance? magnitude m direction south of east

A cylinder that has a 40.0 cm radius and is 50.0 cm deep is filled with air (diatomic) at 20.0∘C and 1.00 atm (part A of the figure below). A 20.0 kg piston is now lowered into the cylinder, quickly compressing the air trapped inside (figure part B). Finally, a 75.0 kg man stands on the piston, further compressing the air (also quickly). (figure part C) (a) How far down does the piston move when the man steps onto it? (b) To what temperature should the gas be heated to raise the piston and man back to the original height of the piston?

A block of mass m = 2.00 kg is at rest on a ramp of mass M = 5.30 kg which, in turn, is at rest on a frictionless horizontal surface (see (a) in the figure). The block and the ramp are aligned so that each has its center of mass located at x = 0. When released, the block slides down the ramp to the left and the ramp, also free to slide on the frictionless surface, slides to the right (see (b) in the figure). Calculate xramp (in m ), the distance the ramp has moved to the right, when xblock = −0.250 m. HINT m

A hungry bear weighing 735 N walks out on a beam in an attempt to retrieve a basket of goodies hanging at the end of the beam (see the figure below). The beam is uniform, weighs 200 N, and is 5.50 m long, and it is supported by a wire at an angle of θ = 60.0∘. The basket weighs 80.0 N. (1) (a) Draw a force diagram for the beam. (Submit a file with a maximum size of 1 MB.) Choose File no file selected This answer has not been graded yet. (b) When the bear is at x = 1.20 m, find the tension in the wire supporting the beam. N When the bear is at x = 1.20 m, find the components of the force exerted by the wall on the left end of the beam. (Assume the positive +x direction is to the right and the positive +y direction is upward. Include the sign of the value in your answer.) Fx = N Fy = N (c) If the wire can withstand a maximum tension of 800 N, what is the maximum distance the bear can walk before the wire breaks? m

A beam resting on two pivots has a length of L = 6.00 m and mass M = 91.0 kg. The pivot under the left end exerts a normal force n1 on the beam, and the second pivot placed a distance ℓ = 4.00 m from the left end exerts a normal force n2. A woman of mass m = 58.5 kg steps onto the left end of the beam and begins walking to the right as in the figure below. The goal is to find the woman's position when the beam begins to tip. (i) (a) Sketch a free-body diagram, labeling the gravitational and normal forces acting on the beam and placing the woman x meters to the right of the first pivot, which is the origin. (Submit a file with a maximum size of 1 MB.) Choose file no file selected This answer has not been graded yet. (b) Where is the woman when the normal force n1 is the greatest? x = m (c) What is n1 when the beam is about to tip? N (d) Use the force equation of equilibrium to find the value of n2 when the beam is about to tip. N (e) Using the result of part (c) and the torque equilibrium equation, with torques computed around the second pivot point, find the woman's position when the beam is about to tip. x = m (f) Check the answer to part (e) by computing torques around the first pivot point. x = m Except for possible slight differences due to rounding, is the answer the same? Yes No

A 1.10 kg solid, uniform ball of radius 0.160 m is released from rest at point A in the figure below, its center of gravity a distance of 1.90 m above the ground. The ball rolls without slipping to the bottom of an incline and back up to point B where it is launched vertically into the air. The ball then rises to its maximum height hmax at point C. HINT (a) At point B, find the ball's translational speed vB (in m/s). m/s (b) At point B, find the ball's rotational speed ωB (in rad/s). rad/s (c) At point C, find the ball's rotational speed ωC (in rad/s). rad/s (d) At point C, find the maximum height hmax of the ball's center of gravity (in m ). m

A student stands at the edge of a cliff and throws a stone horizontally over the edge with a speed of v→0 = 17.5 m/s. The cliff is h = 38.0 m above a flat, horizontal beach as shown in the figure. (a) What are the coordinates of the initial position of the stone? x0 = m y0 = m (b) What are the components of the initial velocity? v0x = m/s v0y = m/s (c) Write the equations for the x-and y-components of the velocity of the stone with time. (Use the following as necessary: t. Let the variable t be measured in seconds. Do not include units in your answer.) vx = vy = (d) Write the equations for the position of the stone with time, using the coordinates in the figure. (Use the following as necessary: t. Let the variable t be measured in seconds. Do not state units in your answer.) x = y = (e) How long after being released does the stone strike the beach below the cliff? s (f) With what speed and angle of impact does the stone land? v→f = m/s θ = ∘ below the horizontal

A 2.30 kg solid, uniform ball of radius 0.160 m is released from rest at point A in the figure below, its center of gravity a distance of 1.60 m above the ground. The ball rolls without slipping to the bottom of an incline and back up to point B where it is launched vertically into the air. The ball then rises to its maximum height hmax at point C. (a) At point B, find the ball's translational speed VB. (b) At point B, find the ball's rotational speed ωB. (c) At point C, find the ball's rotational speed ωC. Note: The rotational speed of the ball does remains same when it rises up, whereas the translational velocity only changes. (d) At point C, find the maximum height hmax of the ball's center of gravity (in m ). Use conservation of energy to solve the problem as the ball has some rotational speed thoughout its motion.

A hungry bear weighing 700 N walks out on a beam in an attempt to retrieve a basket of food hanging at the end of the beam. The beam is uniform, weighs 200 N, and is 7.00 m long; the basket weighs 80.0 N. (a) Draw a free-body diagram for the beam. (Do this on paper. Your instructor may ask you to turn in this sketch.) (b) When the bear is at x = 0.90 m, find the tension in the wire and the components of the force exerted by the wall on the left end of the beam. (tension) (ΣFx) (ΣFy) (c) If the wire can withstand a maximum tension of 900 N, what is the maximum distance the bear can walk before the wire breaks?

Two astronauts, each having a mass M, are connected by a rope of length d having negligible mass. They are isolated in space, orbiting their center of mass at speeds v. (Use any variable or symbol stated above as necessary.) (i) (a) Treating the astronauts as particles, calculate the magnitude of the angular momentum of the two-astronaut system. Li = (b) Calculate the rotational energy of the system. K = By pulling on the rope, one of the astronauts shortens the distance between them to d/10. (c) What is the new angular momentum of the system? Lf = (d) What are the astronauts 1 new speeds? vf = (e) What is the new rotational energy of the system? Kf = (f) How much chemical potential energy in the body of the astronaut was converted to mechanical energy in the system when he shortened the rope? W =

In the figure two tiny conducting balls of identical mass m and identical charge q hang from nonconducting threads of length L. Assume that θ is so small that tan⁡θ can be replaced by its approximate equal, sin⁡θ. If L = 170 cm, m = 7.5 g, and x = 4.4 cm, what is the magnitude of q? Number Units the tolerance is +/−2%

Two charges, q1 = +3.0 nC and q2 = −4.0 nC, are located as shown in the figure. Charge q1 is located on the y-axis at y = 6.0 cm. Charge q2 is at x = 8.0 cm, y = 5.0 cm. a) (5) At the origin, draw the electric field vectors created by each of the charges. b) (10) Calculate the magnitudes of the electric fields created by each of the charges at the origin.

Consider the following figure. (a) Find the equivalent capacitance between points a and b for the group of capacitors connected as shown in the figure above. Take C1 = 2.00 μF, C2 = 13.0 μF, and C3 = 4.00 μF. μF (b) What charge is stored on C3 if the potential difference between points a and b is 60.0 V? μC

The figure below shows the arrangement of three point charges. The force on the −1.0 nC charge is as shown. What is the magnitude of this force? (Please note that 5 cm refers to the full distance between the two bottom charges.)

A simple harmonic oscillator's velocity is given by vy(t) = (0.780 m/s)sin⁡(10.6t − 5.95). Find the oscillator's position, velocity, and acceleration at each of the following times. (Include the sign of the value in your answer.) (a) t = 0 position m velocity m/s acceleration m/s2 (b) t = 0.500 s position m velocity m/s acceleration m/s2 (c) t = 2.00 s position m velocity m/s acceleration m/s2

A non-conductive rod has a uniform positive charge density +λ, a total charge Q along its right half, a uniform negative charge density −λ, and a total charge −Q along its left half, see Fig. below. (a) What is the electric potential at point A? (b) What is the electric potential at point B?

As shown in the figure below, a small, solid, uniform ball is to be shot from point P so that it rolls smoothly along a horizontal path, up along a ramp, and onto a plateau. Then it leaves the plateau horizontally to land on a game board, at a horizontal distance d from the right edge of the plateau. The vertical heights are h1 = 4.70 cm and h2 = 1.60 cm. With what speed must the ball be shot at point P for it to land at d = 6.40 cm? m/s

As shown in the figure, a small particle of charge q = 7.0×10−9 C and mass m = 4×10−12 kg has velocity v0 = 9×103 m/s as it enters a region of uniform magnetic field. The particle is observed to travel in the semicircular path shown, with radius R = 5.0 cm. Calculate the magnitude and direction of the magnetic field in the region.

A cylinder that has a 39.5−cm radius and is 50.0 cm deep is filled with air at 26.5∘C and 1.00 atm shown in figure (a). A 18.0−kg piston is now lowered into the cylinder, compressing the air trapped inside as it takes equilibrium height hi as shown in figure (b). Finally, a 24.0−kg dog stands on the piston, further compressing the air, which remains at 26.5∘C as shown in figure (c). (a) How far down (Δh) does the piston move when the dog steps onto it? mm (b) To what temperature should the gas be warmed to raise the piston and the dog back to hi? ∘C

In the figure, a solid 0.3 kg ball rolls smoothly from rest (starting at height H = 5.9 m) until it leaves the horizontal section at the end of the track, at height h = 2.2 m. How far horizontally from point A does the ball hit the floor?

Three point charges, Q1 = 22.4 μC, Q2 = −33.6 μC, and Q3 = 67.3 μC, are arranged as shown in the figure. The lengths y and x both equal 70.1 cm. Calculate the electric potential V at point A. V = V

For a single, isolated point charge carrying a charge of q = 6.32×10−11 C, one equipotential surface consists of a sphere of radius r1 = 0.0189 m centered on the point charge as shown in the figure. What is the potential on this surface? potential: V Now consider an additional equipotential surface that is separated by 18.4 V from the previously mentioned surface. How far from the point charge should this surface be? This surface must also meet the condition of being farther from the point charge than the original equipotential surface. distance from point charge: m

Two charges are placed on the x axis, equidistant from the y axis. The first charge, q1 = 1.21 μC, is placed at the coordinates (d, 0), and the second charge, q2 = 2.17 μC, is placed at the coordinates (−d, 0) where d = 0.258 m. There is a location on the x axis, (x0, 0), where the net electric field has a magnitude of zero. What is the value, in meters, of x0? x0 = m

Charge q1 = 5.99⋅10−8 C is placed at the origin. Charges q2 = −2.01⋅10−8 C and q3 = 1.79⋅10−8 C are placed at points (0.125 m, 0 m ) and (0 m, 0.219 m), respectively, as shown in the figure. a) Determine the magnitude of the net electrostatic force on charge q3. (You may enter your calculation using scientific notation.) N b) Determine the direction of the net electrostatic force on charge q3. (Enter the angle with respect to the positive x-axis). deg

A particle with charge +q1 and a particle with charge −q2 are located as shown in the figure below. What is the potential (relative to infinity) at location A ? (Use any variable or symbol stated above along with the following as necessary: ε0, r1A, r2A, and r12.) VA =

A block with mass of 10 kg is on a frictionless surface. One hand on the left side of the block is pushing it to the right. A second hand on the right side of the block is pushing it to the left. Hand 1 Hand 2 The block starts from rest. Then Hand 1 pushes with a force of 8 N and the block moves to the right a distance of 4 m, where it has a final velocity of 2 m/s. Between its initial and final positions, how much work did Hand 2 do? −12 J −32 J +12 J +20 J 0 N +32 J −44 J +44 J −20 J

Q 7A: A spring hangs vertically from a bracket at its unweighted equilibrium length, as shown in the left-most image. An object with mass m is attached to the lower end of the spring, and it is gently lowered until the spring reaches its new equilibrium length, as shown in the center figure. Referring to the right-most figure, the mass is raised until the spring returns to its original length, and then it is released from rest resulting in vertical oscillations. Part (a) If the spring constant is 8.9 N/m, and the mass of the object is 0.5 kg, find the oscillation amplitude, in meters. Part (b) Find the maximum velocity, in meters per second, of the oscillating mass. A numeric value is expected

In the figure two tiny conducting balls of identical mass m and identical charge q hang from nonconducting threads of length L. Assume that θ is so small that tan⁡θ can be replaced by its approximate equal, sin⁡θ. If L = 130 cm, m = 9.1 g, and x = 3.8 cm, what is the magnitude of q? Number Units

Find the net torque on the wheel in the figure below about the axle through O perpendicular to the page, taking a = 15.0 cm and b = 29.0 cm. (Indicate the direction with the sign of your answer. Assume that the positive direction is counterclockwise.) N⋅m

A cook holds a 1.90-kg carton of milk at arm's length (see the figure below). What force F→B must be exerted by the biceps muscle? (Ignore the weight of the forearm. Give the magnitude.) N

A 10 kg block is lowered down an incline with an angle of 40 degrees, and a distance of 9 m from point A to point B. A horizontal force F = 10 N is applied to the block between and as shown in the figure. The kinetic energy of the block at A is 20 J and at B, it is 30 J. How much work is done on the block by the force of friction between A and B? J

The figure above shows a circuit containing a battery and three capacitors. The value of the capacitance of the third capacitor is C3 = 1.2 μF and V = 7 V. a) What is the equivalent capacitance in the circuit above? μF b) What charge is stored on the capacitor C1? μC c) What is the voltage across capacitor C1? V d) What is the energy stored in capacitor C1? μJ e) What charge is stored on the capacitor C2? μC f) What is the voltage across capacitor C2? V

A wire with length L = 0.6 m carries a current of I = 6 A in the presence of the following external magnetic potential: V→m = (8 J Am)ϕ^ + ((4 J Am3)z2)ρ^ z = 0 What is the magnetic potential energy (in μJ) associated with the interaction between the electric current and the external magnetic potential? Type your answer. . .

An infinite, nonconducting sheet has a surface charge density σ = +8.09 pC/m2. (a) How much work is done by the electric field due to the sheet if a particle of charge q0 = 8.01×10−19 C is moved from the sheet to a point P at distance d = 3.20 cm from the sheet? (b) If the electric potential V is defined to be zero on the sheet, what is V at P? (a) Number Units (b) Number Units

An inclined plane of angle θ = 20.0∘ has a spring of force constant k = 510 N/m fastened securely at the bottom so that the spring is parallel to the surface as shown in the figure below. A block of mass m = 2.55 kg is placed on the plane at a distance d = 0.273 m from the spring. From this position, the block is projected downward toward the spring with speed v = 0.750 m/s. By what distance is the spring compressed when the block momentarily comes to rest? m

Calculate the speed (in m/s) of an electron and a proton with a kinetic energy of 1.05 electron volt (eV). (The electron and proton masses are me = 9.11×10−31 kg and mp = 1.67×10−27 kg. Boltzmann's constant is kB = 1.38×10−23 J/K.) HINT (a) an electron m/s (b) a proton m/s (c) Calculate the average translational kinetic energy in eV of a 3.25×102 K ideal gas particle. (Recall from Topic 10 that 12 mv2¯ = 32 kBT.) eV

The figure below shows three positively charged particles at three corners of a rectangle. The particle at upper left has a charge q1 = 3.00 nC, the one at the lower left has a charge of q2 = 5.00 nC, and the one at lower right has a charge q3 = 8.00 nC. The rectangle's horizontal side has length x = 6.50 cm and its vertical side has length y = 2.50 cm. (i) (a) What is the electric potential (in V) at the upper-right corner of the rectangle? (Assume the zero of electric potential is at infinity.) V (b) What would be the potential (in V) at the upper-right corner if the charge q2 at lower left was −5.00 nC instead? V

The electric potential at points in an xy plane is given by V = (2.6 V/m2)x2 − (2.8 V/m2)y2. What are (a) the magnitude of the electric field at the point (3.7 m, 2.0 m) and (b) the angle that the field there makes with the positive x direction. (a) Number Units (b) Number Units

A cart starts from position 4 in the figure below with a velocity of 16.6 m/s to the left. As shown, h4 = 20.9 m, h3 = 12.0 m, and h2 = 16.6 m. Find the speed with which the cart reaches positions 3, 2, and 1 (in that order). Neglect friction. Let g = 9.81 m/s2.

A block of mass m1 = 3.46 kg on a frictionless plane inclined at angle θ = 26.0∘ is connected by a cord over a massless, frictionless pulley to a second block of mass m2 = 2.71 kg hanging vertically (see the figure). (a) What is the acceleration of the hanging block (choose the positive direction down)? (b) What is the tension in the cord?

A tiny ball of mass 0.400 g is suspended by a thread of negligible mass in a horizontal electric field of 400 N/C. If the ball has a charge q = 1.35×10−5 C, what will be the deflection angle of the string measured from the vertical? Ball in electric field Figure 16.33 Problems 16.34 and 16.35. (c16p34)

After a mishap, a 62-kg circus performer clings to a trapeze, which is being pulled to the side by another circus artist, as shown above. Calculate the magnitude of the tension in the two ropes if α = 25∘, β = 9∘ and the person is momentarily motionless. You may click the image to enlarge. Help on how to format answers: units. T1 = T2 =

A 1.425−kg block is resting against a light, compressed spring at the bottom of a rough plane inclined at an angle of 36.3∘; the coefficient of kinetic friction between block and plane is μk = 0.131. Suppose the spring is compressed 13.3 cm from its equilibrium length. The spring is then released, and the block separates from the spring and slides up the incline a distance of only 2.85 cm beyond the spring's normal length before it stops. a. Determine the change in total mechanical energy of the system. (Include a minus sign if necessary.) b. Determine the spring constant.

A windmill captures 600W of wind power for 9h. The kinetic energy is converted to electric energy and stored in a battery, before being used by a 60W light bulb. During the process 75% of the energy is lost. wind energy captured: loss: energy delivered to light bulb: W h W h W h How long could the light bulb be used? hours

(a) Figure (a) shows a nonconducting rod of length L = 8.30 cm and uniform linear charge density λ = +9.48 pC/m. Take V = 0 at infinity. What is V at point P at distance d = 6.50 cm along the rod's perpendicular bisector? (b) Figure (b) shows an identical rod except that one half is now negatively charged. Both halves have a linear charge density of magnitude 9.48 pC/m. With V = 0 at infinity, what is V at P? (a) (b) (a) Number i Units (b) Number Units

This is an x-t graph for an object connected to a spring and moving in simple harmonic motion. At which of the following times is the potential energy of the spring the greatest? t = 3T/8 t = T/8 t = T/2 t = T/4

Problem Determine the banking angle θ of the circular track so that the wheels of the sports car shown will not have to depend on friction to prevent the car from sliding either up or down the curve. The car has negligible size and travels at a constant speed of 100 ft/s. The radius of the track is 600 ft.

Two astronauts (figure), each having a mass of 74.0 kg, are connected by a d = 11.0-m rope of negligible mass. They are isolated in space, orbiting their center of mass at speeds of 4.70 m/s. (a) Treating the astronauts as particles, calculate the magnitude of the angular momentum of the two-astronaut system. kg⋅m2/s (b) Calculate the rotational energy of the system. kJ (c) By pulling on the rope, one astronaut shortens the distance between them to 5.00 m. What is the new angular momentum of the system? kg⋅m2/s (d) What are the astronauts' new speeds? m/s (e) What is the new rotational energy of the system? kJ (f) How much chemical potential energy in the body of the astronaut was converted to mechanical energy in the system when he shortened the rope? kJ

The figure below shows a uniformly charged thin rod of length L = 4.51 cm with one half positively charged and the other half negatively charged. Both halves have a linear charge density of magnitude 4.68 nC m. With V = 0.00 at infinity, what is V at point P, located a distance d = 5.40 cm from the rod along the rod's perpendicular bisector? V

Which one of the bar graphs corresponds to the skater at the bottom of a track (position B) that has friction? C A E B D

A 50 kg child stands on the edge of a stationary thin rod of length 5.0 m and mass M = 100 kg, free to rotate around its center of mass O. The child catches a ball of mass 2.0 kg thrown by a friend. Just before the ball is caught, the ball has a horizontal velocity of magnitude 30 ms−1, at angle θ = π/4 with a rod, as shown in Fig. 4 (a) What is the angular speed of the thin rod just after the ball is caught? (b) What is the mechanical energy of the child after the ball has been caught? [6 marks] (c) With what horizontal velocity, at an angle ϕ = π/6 with respect to the rod, has the boy to throw away the ball such that after the launch he will stay at rest? [7 marks]

A rectangular block has its upper right corner carved out. The carved out portion is a quarter of a cylinder, yielding a circular slope of radius R. The remaining block has a mass M. A small bead of mass m is placed at the top of the slope. All contact surfaces are frictionless. Both the small bead and the block are initially at rest, and the bead slides down from the top of the circular slope. (a) Find the displacement of the block, i. e the distance and direction of its movement, when the small bead slides to the bottom of the circular slope and is just about to leave the block. (b) Find the speed of the small bead with respect to the ground when it reaches the bottom of the circular slope.

The drawing shows a collision between two pucks on an air-hockey table. Puck A has a mass of 0.0490 kg and is moving along the x axis with a velocity of +6.01 m/s. It makes a collision with puck B, which has a mass of 0.0980 kg and is initially at rest. The collision is not head-on. After the collision, the two pucks fly apart with the angles shown in the drawing. Find the speed of (a) puck A and (b) puck B. (a) Number Units (b) Number Units

One end of a uniform 3.90-m-long rod of weight Fg is supported by a cable at an angle of θ = 37∘ with the rod. The other end rests against the wall, where it is held by friction as shown in the figure below. The coefficient of static friction between the wall and the rod is μs = 0.575. Determine the minimum distance x from point A at which an additional object, also with the same weight Fg′ can be hung without causing the rod to slip at point A. m

A 1715 kg car accelerates from rest to 21 m/s. What energy E is required to accomplish this? Assume that no dissipative forces act on the car. E = J In terms of to the amount of energy E required to accelerate a car from rest to 21 m/s, how much additional energy ΔE is required to accelerate the car from 21 m/s to twice that speed, 42 m/s ? ΔE = 0 ΔE = 2E ΔE = 3E ΔE = 4E

The mass of a particle is 83 kg. (a) What is its weight on Earth (in N)? N (b) What is its weight on the Moon (in N)? N (c) What is its mass on the Moon (in kg)? kg (d) What is its weight (in N) in outer space far from any celestial body? N (e) What is its mass at this point (in kg)? kg

You are moving and pushing a box up a ramp into your moving truck. The box has a mass of 15.50 kg and the ramp is at an angle of θ = 16.00∘. The ramp and box have a coefficient of friction between them of μk = 0.15. You push the box parallel to the ramp with a force of 300.00 N and you push the box a total distance of 4.40 m (measured along the ramp). Question What is the final velocity of the box after moving 4.40 m along the ramp? Assume that the velocity of the box at the start of the ramp was 2.00 m/s. Your Answer Should Include: 2 Decimal Places Correct SI Units Correct Vector sign (assume +x is to the right)

At a mail sorting facility, packages slide down a ramp but are stopped part way down the ramp so that they can be scanned. While the packages are scanned, they are held in place by a horizontal force from a spring-loaded arm. The ramp makes an angle of θ = 35.5∘ with the horizontal. The package has a mass of 9.75 kg. The coefficient of static friction between the ramp and the package is 0.395 . Calculate the minimum force Fmin that this arm must apply to hold a package on the ramp. Fmin =

The figure shows a solid metal object moving through a uniform magnetic field given by B→ = (2.00×10−2 T)k^. The motion creates a potential difference of 1.30×10−3 V across the object, with the (unseen) left face negatively charged. What is the speed (m/s) of the object? B = 2.00×10−2 T, d1 = 5.00×10−2 m, d2 = 3.00×10−2 m, d3 = 2.00×10−2 m. 4.00 6.00 2.17 8.50 1.30 0.619 2.40 0.929 0.371 3.25

What does φ measure? It is the angle between the velocity and the magnetic field. It is the angle between the magnetic force and the velocity. It is the angle between the magnetic force and the magnetic field.

A charged particle moves through uniform electric and magnetic fields. In which case is there the possibility that the electric force and magnetic force cancel? The electric field is in the same direction as the magnetic field. The electric field and the magnetic field are in opposite directions. The electric field and the magnetic field are perpendicular.

In a Hall effect experiment, how is the potential difference across the width related to the electric field magnitude? The potential difference is the ratio of the width to the field magnitude. The potential difference is the ratio of the field magnitude to the width. The potential difference is the product of the field magnitude and the width.

When an electron circles in a uniform circular motion, which describes its speed? It decreases with each full circle. It increases with each full circle. It remains the same.

In a cyclotron, which describes the kinetic energy of a proton? The proton's kinetic energy increases in the circular dee but not in the gap. The proton's kinetic energy is constant. The proton's kinetic energy does not increase, only the direction of the velocity vector changes. The proton's kinetic energy increases continuously during the spiraling. The proton's kinetic energy increases in the gap but not in the circular dee.

In the Biot-Savart law, which describes angle θ? It is the angle between a current-length element and the magnetic field created by that element. It is the angle between the magnetic field created by a current-length element and a vector directed from that element to the point of measurement. It is the angle between the direction of the current in a current-length element and a vector directed from that element toward the point of measurement.

We set up two parallel currents in the same direction. Which describes the magnetic force on each wire due to the other wire? The force on each current is perpendicular to the current and away from the other current. The force on each current is in the direction of the current. The force on each current is perpendicular to the current and toward the other current. The force on each current is in the direction opposite that of the current.

What do we calculate if we integrate length element ds around a full circle? the area of the circle the diameter of the circle the circumference of the circle the radius of the circle

Which is true about a solenoid? The internal magnetic field is approximately uniform. The external magnetic field is weak. The internal magnetic field is weak. The external magnetic field is approximately uniform. The magnetic field is approximately uniform both inside and outside the solenoid.

Which describes the procedure for finding the magnetic field on the central axis of a current loop due to the elements on the loop? We sum the magnitudes of the magnetic fields. We sum the field components that are perpendicular to the central axis. We sum the field components that are parallel to the central axis.

In a certain mass spectrograph, an ion beam passes through a velocity filter consisting of mutually perpendicular fields: electric field E→ and magnetic field B→. The beam then enters a region of another magnetic field, B′→, which is perpendicular to the ion beam. The radius of curvature of the resulting ion beam will be proportional to what? B/EB′ BB′/E E/BB′ EB′/B EB/B′

In the figure below, i1 = 6.69 A and i2 = 2.21 A. What is the value of the line integral of B→ ? T⋅m This is how to assign a sign to a current used in Ampere's law.

The figure below shows the cross section of three long straight current carrying wires. Wire a carries a current of 5.90 A, wire b carries a current of 4.26 A, and wire c carries a current of 3.04 A. What is the magnitude of ∮B→⋅ds→ for a clockwise Amperian loop that surrounds all three wires? 1.66×10−5 T⋅m 3.14×10−5 T⋅m 8.95×10−6 T⋅m 2.40×10−5 T⋅m

A wire carrying 6.60 A of current is bent into a circular arc with a radius of 0.800 cm. The strength of the magnetic field at the center of the arc is 7.30×10−5 T. What arc does the wire sweep out? radian

An electron is moving in the yz plane, and at a particular instant, the electron has the velocity vector components vy = 5.0×105 m/s and vz = −3.0×105 m/s. The electron is moving through a region of uniform magnetic field with magnitude 0.80 T oriented in the negative y direction. What is the magnetic force experienced by the electron, in newtons, at the instant in question? 6.4×10−14 N in the positive x direction 7.5×10−14 N in the negative x direction 7.5×10−14 N in the positive x direction 3.8×10−14 N in the positive x direction 3.8×10−14 N in the negative x direction

An electron moves in the positive x direction (of a Cartesian coordinate system), through a uniform magnetic field oriented in the negative y direction. In what direction is the magnetic force experienced by the electron? negative z direction No magnetic force is experienced by the electron. positive y direction negative x direction positive z direction

Two long, straight parallel wires are laid on the ground and aligned in the East-west direction. The current in the northern wire is 14.0 A and is heading to the east. The current in the southern wire is 12.0 A and is heading west. They are separated by 0.0480 m. What is the magnitude of the magnetic field 0.0110 m south of the northern most wire? T

A proton with kinetic energy 68.4 MeV is seen to move in a circular path while in a region with a uniform magnetic field. What kinetic energy must an alpha particle (q = +2e, m = 6.64×10−27 kg) have if it is to move in the same circular path as the proton (q = +e, m = 1.67×10−27 kg)? MeV

A hollow cylindrical conductor of inner radius 0.0100 m and outer radius 0.0214 m carries a uniform current of 6.06 A. What is the magnitude of the magnetic field at radius of 0.0200 m? T

The strength of the magnetic field at the center of two concentric current loops is zero. The smaller loop has a radius of 0.0300 m and a current of 5.00 A. The larger current loop carries a current of 29.0 A. What is the radius of the larger loop? m

An electron moves through a uniform magnetic field. The magnetic field is given by B→ = (0.00i^ − 90.5j^ + 50.9k^) mT. At a moment in time when the velocity is v→ = (0.00i^ + vyj^ + 98400.00k^) m/s, the magnetic force acting on the electron is F→ = (2.59i^ + 0.00j^ + 0.00k^)×10−16 N. What is the value of vy? m/s

The figure below shows the cross section of a long cylindrical conducting cylinder of radius a = 0.0887 m. The current density in the cross section is given by J = (5.67×106 A/m3)r. Where inside the cylinder does the magnetic field have a magnitude of 1.88×10−3 T?

A proton (charge e), traveling perpendicular to a magnetic field, experiences the same force as an alpha particle (charge 2e) which is also traveling perpendicular to the same field. The ratio of their speeds, vproton/valpha is: 0.5 1 2 4 8

At one instant an electron (charge = −1.6×10−19 C) is moving in the xy plane, the components of its velocity being vx = 5.0×105 m/s and vy = 3.0×105 m/s. A magnetic field of 0.80 T is in the positive x direction. At that instant the magnitude of the magnetic force on the electron is: ON 3.8×10−14 N 6.0×10−14 N 6.4×10−14 N 1.0×10−13 N

An ion with a charge of +3.2×10−19 C is in region where a uniform electric field of 5×104 V/m is perpendicular to a uniform magnetic field of 0.8 T. If its acceleration is zero then its speed must be: 0 m/s 1.6×10−5 m/s 4.0×105 m/s 6.3×104 m/s any value but 0 m/s

Electrons (mass m, charge −e) are accelerated from rest through a potential difference V and are then deflected by a magnetic field B→ that is perpendicular to their velocity. The radius of the resulting electron trajectory is: (2eV/m)/B B2eV/m (2mV/e)/B B2mV/e none of these

A loop of wire carrying a current of 2.0 A is in the shape of a right triangle with two equal sides, each 15 cm long. A 0.7 T uniform magnetic field is parallel to the hypotenuse. The total magnetic force on the two equal sides has a magnitude of: 0 N 0.21 N 0.30 N 0.41 N 0.51 N

A loop of wire carrying a current of 2.0 A is in the shape of a right triangle with two equal sides, each 15 cm long. A 0.7 T uniform magnetic field is in the plane of the triangle and is perpendicular to the hypotenuse. The resultant magnetic force on the two equal sides has a magnitude of: 0 N 0.21 N 0.30 N 0.41 N 0.51 N

A loop of current-carrying wire has a magnetic dipole moment of 5.0×10−4 A.m2. If the dipole moment makes an angle of 57∘ with a magnetic field of 0.35 T, what is its potential energy? −9.5×10−5 J −1.5×10−4 J −1.8×10−4 J +1.5×10−4 J +9.5×10−5 J

Figure (a) shows an element of length ds = 1.19 μm in a very long straight wire carrying current. The current in that element sets up a differential magnetic field dB→ at points in the surrounding space. Figure (b) gives the magnitude dB of the field for points 2.5 cm from the element, as a function of angle θ between the wire and a straight line to the point. The vertical scale is set by dBs = 60.1 pT. What is the magnitude of the magnetic field set up by the entire wire at perpendicular distance 2.5 cm from the wire? (a) (b) Number Units

A straight conductor carrying a current i = 7.0 A splits into identical semicircular arcs as shown in the figure. What is the magnetic field at the center C of the resulting circular loop, which has a radius of 7.3 cm? Number Units

In the figure, two concentric circular loops of wire carrying current in the same direction lie in the same plane. Loop 1 has radius 1.70 cm and carries 3.60 mA. Loop 2 has radius 2.50 cm and carries 6.40 mA. Loop 2 is to be rotated about a diameter while the net magnetic field B→ set up by the two loops at their common center is measured. Through what angle must loop 2 be rotated so that the magnitude of the net field is 106 nT? Number Units

A current is set up in a wire loop consisting of a semicircle of radius 4.24 cm, a smaller concentric semicircle, and two radial straight lengths, all in the same plane. Figure (a) shows the arrangement but is not drawn to scale. The magnitude of the magnetic field produced at the center of curvature is 47.39 μT. The smaller semicircle is then flipped over (rotated) until the loop is again entirely in the same plane (Figure (b)). The magnetic field produced at the (same) center of curvature now has magnitude 16.02 μT, and its direction is reversed. What is the radius of the smaller semicircle? (a) (b) Number Units

In Figure (a), wire 1 consists of a circular arc and two radial lengths; it carries current i1 = 0.760 A in the direction indicated. Wire 2 , shown in cross section, is long, straight, and perpendicular to the plane of the figure. Its distance from the center of the arc is equal to the radius R of the arc, and it carries a current i2 that can be varied. The two currents set up a net magnetic field B→ at the center of the arc. Figure (b) gives the square of the field's magnitude B2 plotted versus the square of the current i22. The vertical scale is set by Bs2 = 12.7×10−10 T2. What angle is subtended by the arc? (a) (b) Number Units

A particle undergoes uniform circular motion of radius 25.8 μm in a uniform magnetic field. The magnetic force on the particle has a magnitude of 2.28×10−17 N. What is the kinetic energy of the particle? Number Units

A source injects an electron of speed v = 2.0×107 m/s into a uniform magnetic field of magnitude B = 1.9×10−3 T. The velocity of the electron makes an angle θ = 11∘ with the direction of the magnetic field. Find the distance d from the point of injection at which the electron next crosses the field line that passes through the injection point. Number Units

In a certain cyclotron a proton moves in a circle of radius 0.700 m. The magnitude of the magnetic field is 1.70 T. (a) What is the oscillator frequency? (b) What is the kinetic energy of the proton? (a) Number Units (b) Number Units

In the figure, a long straight wire carries a current i1 = 34.4 A and a rectangular loop carries current i2 = 15.1 A. Take a = 0.999 cm, b = 11.7 cm, and L = 23.4 cm. What is the magnitude of the net force on the loop due to i1? Number Units

A circular loop of radius 11 cm carries a current of 22 A. A flat coil of radius 1.1 cm, having 61 turns and a current of 1.9 A, is concentric with the loop. The plane of the loop is perpendicular to the plane of the coil. Assume the loop's magnetic field is uniform across the coil. What is the magnitude of (a) the magnetic field produced by the loop at its center and (b) the torque on the coil due to the loop? (a) Number Units (b) Number Units

Three long wires all lie in an xy plane parallel to the x axis. They intersect the y axis at the origin, y = d, and y = 2d, where d = 9.1 cm. The two outer wires each carry a current of 3.6 A in the positive x direction. What is the magnitude of the force on a 3.4 m section of either of the outer wires if the current in the center wire is 2.6 A(a) in the positive x direction and (b) in the negative x direction? (a) Number Units (b) Number Units

The magnetic field a distance 2 cm from a long straight current-carrying wire is 2×10−5 T. The current in the wire is: 0.16 A 1.0 A 2.0 A 4.0 A 25 A

Two long straight wires pierce the plane of the paper at vertices of an equilateral triangle as shown below. They each carry 2.0 A, out of the paper. The magnetic field at the third vertex (P) has magnitude: 5.0×10−6 T 8.7×10−6 T 1.0×10−5 T 1.7×10−5 T 2.0×10−5 T

In the figure particles 1 and 2 are fixed in place, but particle 3 is free to move. If the net electrostatic force on particle 3 due to particles 1 and 2 is zero and L23 = 3.87L12, what is the ratio q1/q2? Number Units

The figure shows charged particles 1 and 2 that are fixed in place. q1 = −5e, q2 = +3e, d = 0.200 m. At what coordinate should a third charged particle be placed (x = ? m) such that the net force on it is zero? 0.516 −1.38 −0.550 −0.79 0.316 0.687 0.154 0.887 0.100 −0.333

Two particles, each of positive charge q, are fixed in place on a y axis, one at y = d and the other at y = −d. Write an expression that gives the magnitude E of the net electric field at points on the x axis given by x = αd. Determine the value of α that gives (a) the maximum value of E. Determine the values of α that give half the maximum value of E. Let (b) be the lesser of the two values of α, and (c) the greater of the two values. (a) Number Units (b) Number Units (c) Number Units

In the figure, an electron is shot with an initial speed of 1400 m/s from plate A to plate B, where it arrives with a speed of 700 m/s. The plate separation is d = 0.0500 m. What is the magnitude (N/C) of the electric field between the two plates, which is perpendicular to the plates? An electron has mass 9.11×10−31 kg. 6.91×10−6 1.23×10−5 2.56×10−5 5.04×10−3 8.37×10−5 7.67×10−5 1.25×10−5 3.90×10−6 8.12×10−4 7.29×10−6

An electric field given by E→ = 6.2i^ − 3.6(y2 + 4.6)j^ pierces the Gaussian cube of edge length 0.410 m and positioned as shown in the figure. (The magnitude E is in newtons per coulomb and the position x is in meters.) What is the electric flux through the (a) top face, (b) bottom face, (c) left face, and (d) back face? (e) What is the net electric flux through the cube?

Positive charge Q is distributed uniformly throughout an insulating sphere of radius R, centered at the origin. A particle with a positive charge Q is placed at x = 2R on the x axis. The magnitude of the electric field at x = R/2 on the x axis is: Q/72πε0R2 Q/8πε0R2 11Q/18πε0R2 none of these

Two charged particles are shown in part (a) of the figure. Particle 1, with charge q1, is fixed in place at distance d. Particle 2 , with charge q2, can be moved along the x axis. Part (b) of the figure gives the net electric potential V at the origin due to the two particles as a function of the x coordinate of particle 2. The scale of the x axis is set by xs = 8.00 cm. The plot has an asymptote of V = 5.76×10−7 V as x → ∞. What multiple of e gives charge q2? (a) (b) Number Units *e

A particle with a charge of 5.5×10−8 C charge is fixed at the origin. A particle with a charge of −2.3×10−8 C charge is moved from x = 3.5 cm on the x axis to y = 3.5 cm on the y axis. The change in the potential energy of the two-charge system is: 3.2×10−4 J −3.2×10−4 J 9.3×10−3 J −9.3×10−3 J 0 J

In the figure V = 11 V, C1 = 11 μF, and C2 = C3 = 22 μF. Switch S is first thrown to the left side until capacitor 1 reaches equilibrium. Then the switch is thrown to the right. When equilibrium is again reached, how much charge is on capacitor 1? Number Units

If the plate separation of an isolated charged parallel-plate capacitor is doubled: the electric field is doubled the potential difference is halved the charge on each plate is halved the surface charge density on each plate is doubled none of the above

An electric immersion heater normally takes 110 min to bring cold water in a well-insulated container to a certain temperature, after which a thermostat switches the heater off. One day the line voltage is reduced by 8.00% because of a laboratory overload. How long does heating the water now take? Assume that the resistance of the heating element does not change. Number Units

In the figure current is set up through a truncated right circular cone of resistivity 763 Ω⋅m, left radius a = 2.00 mm, right radius b = 2.48 mm, and length L = 2.25 cm. Assume that the current density is uniform across any cross section taken perpendicular to the length. What is the resistance of the cone? Number Units

If the current density in a certain wire is given by J = J0r/R, where r is the radial distance, R is the wire's radius 2.00 mm, and J0 is 16.0 A/m2, then how much current (A) is between r = 0.200R and r = 0.300R? 4.89×10−5 5.16×10−6 4.21×10−5 1.57×10−6 9.18×10−6 2.55×10−6 6.76×10−5 8.08×10−6 1.99×10−7 7.11×10−5

In the figure the current in resistance 6 is i6 = 1.48 A and the resistances are R1 = R2 = R3 = 1.89 Ω, R4 = 15.6 Ω, R5 = 7.39 Ω, and R6 = 3.68 Ω. What is the emf of the ideal battery? Number Units

In the figure battery 1 has emf E1 = 16.0 V and internal resistance r1 = 0.045 Ω and battery 2 has emf E2 = 16.0 V and internal resistance r2 = 0.020 Ω. The batteries are connected in series with an external resistance R. (a) What R value makes the terminal-to-terminal potential difference of one of the batteries zero? (b) Which battery is that? (a) Number Units (b)

The figure shows a solid metal rectangular object moving in the positive direction of an x-axis, through a uniform magnetic field in the positive direction of the y-axis. What potential difference (V) is set up across the object due to the motion? B = 5.00×10−2 T, v = 5.00×103 m/s in positive x direction d1 = 4.00×10−3 m, d2 = 3.00×10−3 m, d3 = 2.00×10−3 m. 0.080 0.120 0.160 0.400 0.240 0.750 0.060 1.00 0.500 0.310

The figure shows an infinitely long straight wire carrying a current of 5.00 A and a rectangular loop of wire carrying a current of 12.0 A. What is the magnitude (N) of the net magnetic force on the rectangular loop? L = 0.500 m, d1 = 4.00 cm, d2 = 8.00 cm. 9.11×10−4 9.02×10−5 5.13×10−4 4.02×10−5 8.20×10−4 7.50×10−5 1.50×10−4 1.11×10−5 2.25×10−4 2.33×10−5

The current density inside a long, solid, cylindrical wire of radius 2.50 mm is in the direction of the central axis and its magnitude varies with radial distance r from the axis as J = (2.50×109 A/m4)r2. Find the magnitude of the magnetic field (T) 4.00 mm from the central axis. 2.02×10−5 1.63×10−5 3.91×10−5 5.03×10−5 2.75×10−5 8.19×10−5 9.09×10−6 4.26×10−5 7.67×10−6 1.25×10−5

An electron is released from rest at the negative plate of a parallel plate capacitor and accelerates to the positive plate (see the drawing). The plates are separated by a distance of 1.7 cm, and the electric field within the capacitor has a magnitude of 2.1×106 V/m. What is the kinetic energy of the electron just as it reaches the positive plate? KEpositive =

A 0.75 kg block is fired by a spring gun toward a ramp angled 15 degrees above the horizontal with a coefficient of friction of 0.15. The block reaches the ramp base with an initial velocity of vo. As the block goes up the ramp it slows and stops after it has traveled 0.80 meters along the ramp. Draw a diagram of the forces on the block in the space below. Use work-energy arguments to answer the following questions. a) The work in Joules done on the block by gravity as it slides up the ramp is ? Show work. b) The work done in Joules by friction on the block as it slides up the ramp is ? Show work. c) The total work done in Joules on the box by both friction and gravity is ? d) How is the work done on the block related to the kinetic energy of the block at the bottom of the ramp? Explain briefly. e) How fast was the block initially moving in m/s at the bottom of the ramp? Show work.

An isolated conductor has a net charge of +11.0× 10−6 C and a cavity with a particle of charge q = +2.30×10−6 C. What is the charge (a) on the cavity wall and (b) on the outer surface?

Two blocks are connected by a negligible mass string passing over a frictionless pulley of radius R = 0.1 m and moment of inertia I = 0.02 kgm2. A 64.8 N horizontal force acts on the 8.00−kg object. The 8 kg block moves to the right with a constant linear acceleration a. The coefficient of kinetic friction between the horizontal surface and the 8 kg block μk is 0.5. Determine (a) the linear acceleration a of the system, (b) T1 and T2 the tensions in the two parts of the string.

A flat, 179-turn, current-carrying loop is immersed in a uniform magnetic field. The area of the loop is 4.53 cm2 and the angle between its magnetic dipole moment and the field is 32.3∘. Find the strength B of the magnetic field that causes a torque of 2.27×10−5 N⋅m to act on the loop when a current of 2.07 mA flows in the loop. B = T

(a) Given a 52.0 V battery and 32.0 Ω and 60.0 Ω resistors, find the current (in A ) and power (in W ) for each when connected in series. I32.0 Ω = A P32.0 Ω = W I60.0 Ω = A P60.0 Ω = W (b) Repeat when the resistances are in parallel. I32.0 Ω = A P32.0 Ω = W I60.0 Ω = A P60.0 Ω = W

A yoga instructor completes a triangle pose as shown in the figure. His left foot is planted 30 cm away from the vertical line passing through his centre of gravity. His right foot is 60 cm away. The instructor's mass is 68 kg. The centre of gravity is located as shown in the figure. HINT: Remember that one can choose ANY point as the origin for torque. Just be consistent and use the same origin for all torques. (a) What is the normal force acting on the instructor's left foot? N (b) What is the normal force acting on the instructor's right foot? N In order to go deeper, the instructor uses his abductor muscles. They exert a force on each leg outwards (away from the midplane of the body). The coefficient of static friction between the legs and the mat is .60. (c) What is the minimum force to be exerted on the left foot to slide it outwards? N (d) What is the minimum force to be exerted on the right foot to slide it? N

The figure shows an initially stationary block of mass m on a floor. A force of magnitude 0.500 mg is then applied at upward angle θ = 15.0∘. What is the magnitude of the acceleration of the block across the floor if the friction coefficients are (a) static = 0.600 and kinetic = 0.500 and (b) static = 0.400 and kinetic = 0.300?

A 3.5-gram ping-pong ball with charge q is hanging static from an infinite plane of charge, using a nonconducting 25−cm long massless string, as shown below. The angle of the string with the plane is 20 degree, and plane itself makes angle of 30 degree with horizontal. What is the magnitude of the charge q if the surface charge density of the infinite plane of charge is 16 μC/m2? Hint: Draw the free-body diagram of the ping-pong ball.

Figure a shows a rod of resistive material. The resistance per unit length of the rod increases in the positive direction of the x axis. At any position x along the rod, the resistance dR of a narrow-differential-section of width dx is given by dR = 5.00xdx, where dR is in ohms and x is in meters. Figure b shows such a narrow section. You are to slice off a length of the rod between x = 0 and some position x = L and then connect that length to a battery with potential difference V = 5.0 V (Fig. c). You want the current in the length to transfer energy to thermal energy at the rate of 3.2 W. At what position x = L in meters should you cut the rod? Keep 2 decimal points in your answer.

A 46.6-g golf ball is driven from the tee with an initial speed of 40.8 m/s and rises to a height of 28.8 m. (a) Neglect air resistance and determine the kinetic energy of the ball at its highest point. (b) What is its speed when it is 8.99 m below its highest point? (a) Number Units (b) Number Units

A wrecking ball swings at the end of a 11.0-m cable on a vertical circular arc. The crane operator manages to give the ball a speed of 11.8 m/s as the ball passes through the lowest point of its swing and then gives the ball no further assistance. Friction and air resistance are negligible. What speed vf does the ball have when the cable makes an angle of 21.0∘ with respect to the vertical? Number Units

Multiple-Concept Example 11 provides some pertinent background for this problem. A pendulum is constructed from a thin, rigid, and uniform rod with a small sphere attached to the end opposite the pivot. This arrangement is a good approximation to a simple pendulum (period = 0.92 s ), because the mass of the sphere (lead) is much greater than the mass of the rod (aluminum). When the sphere is removed, the pendulum no longer is a simple pendulum, but is then a physical pendulum. What is the period of the physical pendulum? Number Units

Consider the five different simple pendula (labeled A through E) shown below. The figure shows each pendula sitting in its rest position. The length and mass of each simple pendulum is given in terms of a general length L and mass m. For parts (a) and (b) of this problem, suppose that each of the five pendula are released from rest at the same angle φ relative to each pendulum's vertical position. These are all simple pendula! The difference in size of each mass is not relevant. Part (a) If all five pendula are released from rest at the same angle φ (relative to each pendulum's vertical position), rank from first to last the order in which the five pendula will first pass through its vertical position. Support your reasoning. (8 points) Part (b) If all five pendula are released from rest at the same angle φ (relative to each pendulum's vertical position), rank from largest to smallest the speed of each pendulum when it first passes through its vertical position. Support your reasoning. (6 points) Part (c) Now, suppose that each of the five masses is attached to an identical spring with restoring constant k. Rank from largest to smallest the angular frequency of oscillation for each of the masses. Support your reasoning. (6 points)

A playground carousel is rotating counterclockwise about its center on frictionless bearings. A person standing still on the ground grabs onto one of the bars on the carousel very close to its outer edge and climbs aboard. Thus, this person begins with an angular speed of zero and ends up with a nonzero angular speed, which means that he underwent a counterclockwise angular acceleration. The carousel has a radius of 1.52 m, an initial angular speed of 3.23 rad/s, and a moment of inertia of 128 kg⋅m2. The mass of the person is 41.5 kg. Find the final angular speed of the carousel after the person climbs aboard. ωf =

A soccer player kicks a soccer ball of mass 0.45 kg that is initially at rest. The player's foot is in contact with the ball for 1.30×10−3 s, and the force of the kick is given by F(t) = [(6.68×105)t − (5.14×108)t2] N for 0 ≤ t ≤ 1.30×10−3 s, where t is in seconds. Find the magnitudes of the following: (a) the impulse on the ball due to the kick, (b) the average force on the ball from the player's foot during the period of contact, (c) the maximum force on the ball from the player's foot during the period of contact, and (d) the ball's speed immediately after it loses contact with the player's foot. (a) Number Units (b) Number Units (c) Number Units (d) Number Units (d) Number Units

The figure shows a ball with mass m = 0.50 kg attached to the end of a thin rod with length L = 1.8 m and negligible mass. The other end of the rod is pivoted so that the ball can move in a vertical circle. (a) What initial speed must be given the ball so that it reaches the vertically upward position with zero speed? What then is its speed at (b) the lowest point and (c) the point on the right at which the ball is level with the initial point? (d) If the ball's mass were doubled, what would the answer to (a) be? (a) Number Units (b) Number Units (c) Number Units (d) Number Units

A uniformly charged solid sphere with a radius of 0.6 m and net electric charge of 450 nC is rotating with angular speed of 3 rad/s. The axis of rotation is indicated by the dashed line. The magnitude of the constant external magnetic field has a magnitude of 7 mT. What is the magnitude of dipole contribution to the net torque (in pNm ) exerted on the sphere due to its interaction with the external magnetic field if θ = 60∘?