The square loop shown in FIGURE P30.52 moves into a 0.80 T magnetic field at a constant speed of 10 m/s. The loop has a resistance of 0.10 Ω, and it enters the field at t = 0 s. a. Find the induced current in the loop as a function of time. Give your answer as a graph of I versus t from t = 0 s to t = 0.020 s. b. What is the maximum current? What is the position of the loop when the current is maximum? Figure P30.52
A 210-m-wide river flows due east at a uniform speed of 4.1 m/s. A boat with a speed of 7.1 m/s relative to the water leaves the south bank pointed in a direction 27∘ west of north. What is the (a) magnitude and (b) direction of the boat's velocity relative to the ground? Give the direction as the angle of the velocity from due north, positive if to the east and negative if to the west. (c) How long does it take for the boat to cross the river? (a) Number Units (b) Number Units (c) Number Units
A constant horizontal force F→a pushes a 8.70 kg FedEx package across a frictionless floor on which an xy coordinate system has been drawn. The figure gives the package's x and y velocity components versus time t. What are the (a) magnitude and (b) direction of F→a? Give the direction as a positive or negative angle of magnitude less than 180∘ relative to the +x-axis. (a) Number Units (b) Number Units
A train at a constant 77.0 km/h moves east for 35.0 min, then in a direction 51.0∘ east of due north for 23.0 min, and then west for 45.0 min. What are the (a) magnitude and (b) angle (relative to east) of its average velocity during this trip? (a) Number Units (b) Number Units
A point charge q and uniform line charge (of length a and charge density λ) are oriented as shown in the figure below. The point charge is located at distance 2 a from the end of the line charge. A positron p is placed at the position shown, and experiences a total force F→ in the direction indicated. You are given that a = 3.80 cm, and that the magnitude of q is |q| = 4.60 μC. a) What are the signs of q and λ? Explain. b) What is the charge density λ of the line charge, in C/m? c) What is the magnitude F of the force on the positron, in N?
A block of mass m = 2.37 kg is attached to a spring with spring constant k = 835 N/m. It is initially at rest on an inclined plane that is at an angle of θ = 28.3∘ with respect to the horizontal, and the coefficient of kinetic friction between the block and the plane is μk = 0.15. In the initial position, where the spring is compressed by a distance of d = 0.106 m, the mass is at its lowest position and the spring is compressed the maximum amount. Take the initial gravitational potential energy of the block as zero.
What are (a) the x component and (b) the y component of a vector a→ in the xy plane if its direction is 233∘ counterclockwise from the positive direction of the x axis and its magnitude is 7.8 m? (a) Number Units (b) Number Units
A sprinter explodes out of the starting block with an acceleration of +2.01 m/s2, which she sustains for 1.16 s. Then, her acceleration drops to zero for the rest of the race. What is her velocity at (a)t = 1.16 s and (b) at the end of the race? (a) Number Units (b) Number Units
In the figure, a ball is thrown leftward from the left edge of the roof, at height h above the ground. The ball hits the ground 1.80 s later, at distance d = 22.0 m from the building and at angle θ = 60.0∘ with the horizontal. (a) Find h. (Hint: One way is to reverse the motion, as if on videotape.) What are the (b) magnitude and (c) angle relative to the horizontal of the velocity at which the ball is thrown (positive angle for above horizontal, negative for below)? (a) Number Units m (b) Number Units (c) Number Units
There are approximately 107 million TVs in the United States. Each uses, on average, 77 W of power and is turned on for 6.5 hours a day. If electrical energy costs 0.078 dollars per KWh, how much money is spent every day in keeping the TVs turned on? Number Units
Given two particles with Q = 1.70−μC charges as shown in the figure below and a particle with charge q = 1.24×10−18 C at the origin. (Note: Assume a reference level of potential V = 0 at r = ∞.) (a) What is the net force exerted by the two 1.70−μC charges on the test charge q? (b) What is the electric field at the origin due to the two 1.70−μC particles? N/C (c) What is the electrical potential at the origin due to the two 1.70−μC particles? kV
Assume the magnitude of the electric field on each face of the cube of edge L = 1.06 m in the figure below is uniform and the directions of the fields on each face are as indicated. (Take E1 = 34.2 N/C and E2 = 26.1 N/C.) (a) Find the net electric flux through the cube. N⋅m2/C (b) Find the net charge inside the cube. C
A net external force is applied to a 4.27-kg object that is initially at rest. The net force component along the displacement of the object varies with the magnitude of the displacement as shown in the drawing. What is the speed of the object at s = 20.0 m? vf =
During fireworks display, a shell is shot into the air with an initial speed of |v→0| = 70 m/s at an angle of 75.0∘ above the horizontal, as illustrated on the figure. The fuse is timed to ignite the shell just as it reaches its highest point above the ground. Compute the horizontal v0 x and vertical v0 y components of the initial velocity. (2 points)Using the correct equation compute the maximum height h that the shell will reach. (2 points)Using the correct equation compute the time the shell will take to reach the maximum height h. (2 points)Compute the horizontal displacement Δx. (2 points)
What is the minimum uncertainty in an electron's velocity (Δvmin) if the position is known within 11Å. m/s What is the minimum uncertainty in a helium atom's velocity (Δvmin) if the position is known within 1.2Å. Δvmin = m/s
A block of mass m is released from rest at the top of an inclined plane which has a height h = 1 m and an angle θ = 30∘. Assume the inclined plane and the horizontal plane are smoothly connected and there is no impact on the block when it gets on the horizontal plane. It travels another distance d = 2 m and stops. a) Draw the free-body diagrams when the block is on the inclined plane, and when the block is on the horizontal plane. b) If the coefficients of kinetic friction between the block and both planes are the same, find their magnitude.
In the circuit of the figure below, the switch S has been open for a long time. It is then suddenly closed. Take E = 10.0 V, R1 = 41.0 kΩ, R2 = 185 kΩ, and C = 14.0 μF. (a) Determine the time constant before the switch is closed. s (b) Determine the time constant after the switch is closed. s (c) Let the switch be closed at t = 0. Determine the current in the switch as a function of time. (Assume I is in A and t is in s. Do not enter units in your expression. Use the following as necessary: t.)
In the figure, a ball is thrown leftward from the left edge of the roof, at height h above the ground. The ball hits the ground 2.40 s later, at distance d = 22.0 m from the building and at angle θ = 64.0∘ with the horizontal. (a) Find h. (Hint: One way is to reverse the motion, as if on videotape.) What are the (b) magnitude and (c) angle relative to the horizontal of the velocity at which the ball is thrown (positive angle for above horizontal, negative for below)?
A sinusoidal wave moving along a string is shown twice in the figure, as crest A travels in the positive direction of an x axis by distance d = 6.00 cm in 4.30 ms. The tick marks along the axis are separated by 10.0 cm ; height H = 6.60 mm. If the wave equation is of the form y(x, t) = ymsin(kx ± ωt), what are (a) ym, (b) k, (c) ω, and (d) the correct choice of sign in front of ω? (a) Number mm (b) Number Units (c) Number Units (d)
An ant crawls on the floor along the curved path shown in the figure below. (Assume that the ant's initial motion is parallel to the y-axis and its final motion is parallel to the x-axis.) The ant's positions and velocities are incdicated for times tf = 0 and tf = 5.20 s. Determine the x- and y-components of the ant's displacement, average velocity, and average acceleration between the two times. HINT (a) displacement (in m) Δx = m Δy = m (b) average velocity (in m/s) vav,x = m/s vav,y = m/s (c) average acceleration (in m/s2) aav,x = m/s2 aav,y = m/s2
The engine in an imaginary sports car can provide constant power to the wheels over a range of speeds from 0 to 120 kilometers per hour (km/h). At full power, the car can accelerate from zero to 60.0 km/h in time 1.00 s. Part A At full power, how long would it take for the car to accelerate from 0 to 120 km/h? Neglect friction and air resistance. Express your answer in seconds. View Available Hint(s) Submit
Flying Circus of Physics A salamander of the genus Hydromantes captures prey by launching its tongue as a projectile: The skeletal part of the tongue is shot forward, unfolding the rest of the tongue, until the outer portion lands on the prey, sticking to it. The figure shows the acceleration magnitude a versus time t for the acceleration phase of the launch in a typical situation. The indicated accelerations are a2 = 380 m/s2 and a1 = 125 m/s2. What is the outward speed of the tongue at the end of the acceleration phase? Number Units
A uniform electric field of magnitude 280 V/m is directed in the negative y direction as shown in the figure below. The coordinates of point A are (-0.500, -0.700) m, and those of point (B) are (0.550, 0.650)m. Calculate the electric potential difference VB - VA using the dashed-line path. V
Over a certain region of space, the electric potential is V = 6x − 4x2y + 6yz2 (a) Find the expressions for the x, y, z components of the electric field over this region. (Use any variable or symbol stated above as necessary.) Ex = Ey = Ez = (b) What is the magnitude of the field at the point P that has coordinates (1.00, 0, −3.00)m? N/C
Two points, A and B, are separated by 0.0356 m. The potential at A is +86.0 V, and that at B is +44.4 V. Find the magnitude of the constant electric field between the points. Number Units
You are working as an intern for a meteorological laboratory. You are out in the field taking measurements from a balloon that is carrying equipment designed to measure electric fields in the atmosphere. Your supervisor has asked you to determine the average volume charge density at a certain height in the air. When the balloon is at an altitude of 600 m above the ground, the electric field is measured to be 120 N/C directed downward. At 700 m above the ground, the electric field is 110 N/C downward. (a) Determine the average volume charge density (in C/m3) in the layer of air between these two elevations. (Enter the magnitude.) C/m3
In motion in the +x direction, you exert a force of magnitude 25 N on an object for 3 seconds, and observe that the magnitude of the object's momentum decreases by 75 kg⋅m/s. If instead you had exerted a force of magnitude 12.5 N on the object for 3 seconds, what would the magnitude of the object's momentum change have been? (Assume the direction of the second force is the same as the direction of the first force.)
The large block shown is x = 20.0 cm wide, y = 21.0 cm long, and z = 27.00 cm high with a mass of 4.55 kg. This block is passing through air (density of air ρair = 1.43 kg/m3). Calculate the terminal velocity of the block if it is traveling downward with a drag coefficient of Γ = 0.832. See the hint panel for the drag force equation. terminal velocity: m/s
(1) (5pt) For the situation above, assume the coefficients of static and kinetic friction are μ = 0.200, and the block's mass is m = 2.00 kg. The block is on the floor at the Earth's surface. a. Draw a free body diagram for the block showing all the forces. (2pt) b. Write two equations force equations (Newton's 1st and 2nd Laws) for the vertical and horizontal directions. (2pt) c. Find the block's acceleration. (3pt) d. Assume the block is initially at rest. How long does it take for the block to go 10.0 m? (3pt)
Boxes A (mA = 10 kg) and B (mB = 15 kg) are linked together by a rope and pulley as shown in the figure below. Box B falls while pulling box A to the right across a rough surface (μk = 0.2). This problem is similar to the example we covered in lecture, but the masses are different and we now need to account for the kinetic friction acting on box A. Assume the +x direction is towards the right and the +y direction is up. a) Draw the interaction diagram. Make sure to account for all interactions, including friction. (Hint: There are 5 interactions total) b) Draw the free-body diagrams for boxes A and B. Make sure to draw a dashed line to connect any action/reaction force pairs. (Hint: There are four forces acting on box A, and two forces acting on box B) c) Using Newton's second law (F→ = ma→), write the x and y components of the net forces for both boxes. d) Find the value for the acceleration of the boxes.
Suppose you have a 9.50 V battery, a 2.45 μF capacitor, and a 7.25 μF capacitor. (a) Find the charge (in C) and energy (in J) stored if the capacitors are connected to the battery in series. charge C energy J (b) Do the same for a parallel connection. charge C energy J
An elevator car of mass 810 kg falls from rest 3.30 m, hits a buffer spring, and then travels an additional 0.350 m, as it compresses the spring by a maximum of 0.350 m. What is the force constant of the spring?
The figure below shows an object with mass m = 5.5 kg pulled up a plane inclined at an angle of θ = 27∘ with a force of magnitude F = 35 N parallel to the plane. (a) If there is no friction between the object and the plane, what is the magnitude of the object's acceleration (in m/s2)? m/s2 (b) If instead the coefficient of kinetic friction between the object and the plane is 0.12, what is the magnitude of the object's acceleration (in m/s2)? m/s2
Two objects are connected by a light string that passes over a frictionless pulley as shown in the figure below. m1 = 5.84 kg, m2 = 7.30 kg, and φ = 59∘. When released from rest, m1 accelerates downward at 0.884 m/s2. For this to happen, the coefficient of kinetic friction must be , and to even begin sliding in the first place the coefficient of static friction must be ---Select--- than . Use g = 9.8 m/s2
(8%) Problem 3: Suppose you first walk 10.5 m in a direction 20∘ west of north and then 22.5 m in a direction 40∘ south of west as shown in the figure. 25% Part (a) What is the component of your displacement in the x -direction, in meters? 25% Part (b) What is the component of your displacement in the y-direction, in meters? 25% Part (c) How far are you from your starting point in meters? 25% Part (d) What is the angle of a line connecting your starting position to your final position, measured South of West, in degrees? θ =
Net force Three forces are applied to an object, as shown in the figure. Find the magnitude and direction of the sum of the forces.
A crate of mass 9.2 kg is pulled up a rough incline with an initial speed of 1.46 m/s. The pulling force is 98 N parallel to the incline, which makes an angle of 20.5∘ with the horizontal. The coefficient of kinetic friction is 0.400, and the crate is pulled 4.98 m. (a) How much work is done by the gravitational force on the crate? J (b) Determine the increase in internal energy of the crate-incline system owing to friction. J (c) How much work is done by the 98−N force on the crate? J (d) What is the change in kinetic energy of the crate? J (e) What is the speed of the crate after being pulled 4.98 m? m/s
The observer is in air nearly above the object submerged in water (index of refraction 1.33). The depth of the object is 8.1 cm. Find the apparent depth of the object. (Hint: Use Snell's law of refraction and the fact that the angles of incidence and refraction are small, so tan θ ≈ sinθ.) Number Units
The forces in (Figure 1) act on a 2.0 kg object. Part A What is the value of ax, the x-component of the object's acceleration? Express your answer with the appropriate units. Submit Request Answer Part B What is the value of ay, the y-component of the object's acceleration? Express your answer with the appropriate units. Submit Request Answer Figure 1 of 1
The figure shows an x−t graph for some object. x(m) At t = 4 s, what is the distance d of the object from its position at t = 0 s? d = m At about what time ts is the object's speed greatest? ts = s What is the velocity vx of the object between t = 2 s and t = 4 s? vx = m/s
Let g = 9.8 m/s2. A hydraulic system is used to lift a 91 kg motor in a garage. If the motor sits on a piston of area 0.25 m2, and a force is applied to a piston of area 94 cm2, what is the minimum force that must be applied to lift the motor in units of N? Enter a number with one digit behind the decimal point.
Use the model for projectile motion, assuming there is no air resistance and g = 9.8 meters per second per second. A projectile is fired from ground level at an angle of 8∘ with the horizontal. The projectile is to have a range of 49 meters. Find the minimum initial speed necessary. (Round your answer to one decimal place.) m/sec