A bullet of mass 4.55 g moving with a velocity of 505 ms−1 strikes a wooden block of mass 2.95 kg which is suspended vertically from a long cord, as shown in the accompanying diagram. The bullet is embedded in the block and the two move off with the same velocity. Find : 3.1 the momentum of the bullet at the instant before it collides with the block; 3.2 the kinetic energy of the bullet at the instant before it collides with the block; 3.3 the velocity of the block at the instant immediately after the collision occurs 3.4 the maximum height through which the block swing
A small toy car of mass m = 0.05 kg is placed on a rough surface and compressed against a spring with spring constant k = 20 N/m. The equilibrium length of the spring is x0 = 0.25 m, and it is compressed to a length of x1 = 0.1 m. After the car is released, the magnitude of kinetic friction between the car and the spring is f = 1 N. When the spring extends back to a length of x2 = 0.2 m, what is the magnitude of the toy car's velocity? Pick the correct answer v = 2 m/s v = 0 m/s v = 3.46 m/s v = 2.8 m/s v = 2.24 m/s
Calculate the work done in carrying a +10(μC) charge from point P1 to P2 in the figure in existence of the field E = axy - ayx (the distances are in m)? (25%)
In the figure, a 4.1 kg block is accelerated from rest by a compressed spring of spring constant 630 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 = 0.299. The frictional force stops the block in distance D = 8.2 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
In the figure, a 3.5 kg block is accelerated from rest by a compressed spring of spring constant 630 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 = 0.281. The frictional force stops the block in distance D = 7.6 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 block of mass m = 3.30 kg slides along a horizontal table with velocity v0 = 4.50 m/s. At x = 0, it hits a spring with spring constant k = 28.00 N/m and it also begins to experience a friction force. The coefficient of friction is given by μ = 0.350. How far has the spring compressed by the time the block first momentarily comes to rest? Assume the positive direction is to the right. Δx = m
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
A particle of charge Q traveling at velocity V0 enters a uniform magnetic field of width d and homogeneous strength B0 at point P1, as shown in the diagram above. T seconds later the particle exits the field at point P2, a total distance of d away from point P1 as measured strictly along the axis parallel to V0. Assuming the direction of the uniform magnetic field is perpendicular to V0, derive an explicit formula for the angle of deflection θ in this scenario.
An RLC circuit such as that of Figure (a) has R = 6.84 Ω, C = 16.5 μF, L = 1.03 H, and E = 38.6 V. (a) At what angular frequency ωd will the current amplitude have its maximum value, as in the resonance curves of Figure (b)? (b) What is this maximum value? At what (c) lower angular frequency ωd1 and (d) higher angular frequency ωd2 will the current amplitude be half this maximum value? (e) What is (ωd2 - ωd1)/ωd, the fractional half-width of the resonance curve for this circuit? (a)
An RLC circuit such as that in Figure (a), has R = 5.01 Ω, C = 20.4 μF, L = 1.14 H. The fractional half-width Δωd of a resonance curve, such as the ones in Figure (b), is the width of the curve at half the maximum value of I. Find Δωd/ωd Number Units
The drive propeller of a ship starts from rest and accelerates at 2.23×10−3 rad/s2 for 2.81 x 103 s. For the next 1.35×103 s the propeller rotates at a constant angular speed. Then it decelerates at 2.28×10−3 rad/s2 until it slows (without reversing direction) to an angular speed of 2.55 rad/s. Find the total angular displacement of the propeller. Number Units
If v = 25 m/s is the maximum possible speed the car is moving without skidding off the road, what is the friction coefficient between rubber and the road shown in the sketch?
In the figure shown below, a 250.0 g metal bar, 1.5 m long and itself having a resistance of 10.0 Ω, rests horizontally on conducting rails. The bar, which is free to slide along the rails, is in a uniform magnetic field of magnitude 1.75 T. What is the acceleration of the bar when the switch S is closed? a.) 3.6 m/s2 b.) 5.1 m/s2 c.) 7.7 m/s2 d.) 9.5 m/s2 e.) none of these
Tom enlists the help of his friend John to move his car. They apply forces to the car as shown in the diagram. Here |F1| = 432 N, |F2| = 355 N and friction is negligible. Mass of the car = 3.50 103 kg, θ1 = 12.0°, and θ2 = 25.0°. The diagram below shows the top view of the car which is in the x−z plane (horizontal plane). (a) Find the resultant force exerted on the car. (Express your answer in vector notation.) F→net = N (b) What is the acceleration of the car? (Express your answer in vector notation.) a→ = m/s2
A car of mass 1500 kg travels in a circle of radius 50 m at a speed of 20 m/s. It is on a track that is banked (sloped) towards the inside of the curve at an angle of 15∘ with the horizontal. The coefficient of static friction between the car and the slope is μ = 0.70.
A 1000-kg car rounds a curve on a flat road of radius 50 m at a speed of 15 m/s (54 mi/h). Will the car follow the curve, or will it skid? Assume: (a) the pavement is dry and the coefficient of static friction is μs = 0.60; (b) the pavement is icy and (a) μs = 0.25
A thin, 50.0 -cm-long metal bar with mass 75 g rests on, but is not attached to, two metallic supports in a uniform 0.800 T magnetic field, as shown in. A battery and a 10.00 Ω resistor in series are connected to the supports. What is the highest voltage the battery can have without breaking the circuit at the supports? Neglect the resistance of the bar. (Take g = 10 m/s2) 3.8 V 9.4 V 18.8 V 52.5 V 507.0 V
Tom enlists the help of his friend John to move his car. They apply forces to the car as shown in the diagram. Here F1 = 427 N and F2 = 380 N and friction is negligible. In the diagram below, the mass of the car = 3500 kg, θ1 = −25∘ and θ2 = 12∘. (Assume the car faces the positive x-axis before the forces are applied.) (a) Find the resultant force (in N) exerted on the car. magnitude N direction (counterclockwise from the +x-axis) (b) What is the acceleration (in m/s2) of the car? magnitude m/s2 direction (counterclockwise from the +x-axis) ∘
A car is rolling over the top of a hill at constant speed v as shown in the figure. If n is the normal reaction force of the ground on the car, and w is the weight of the car. Which of the following is true at this instant? (there may be more than one true answer) w > n w < n w = n The velocity and acceleration are perpendiculars to each other. The acceleration of the object is zero
An electron with a horizontal speed of 2500000 m/s and no vertical component of velocity passes through two horizontal parallel plates, as shown. The magnitude of the electric field between the plates is 180 N/C. The plates are 5 cm long. Calculate the angle to the horizontal, θ (in degrees), that the electron would pass through the plates with. Attach your work for full marks. Answers within 3% of the true answer will be considered correct. Your Answer:
See the 3 charges arranged in an equilateral triangle below. Each charge has a magnitude of 3 nC, and are separated on each side by 0.5 meters. Calculate the net electric field in component form at the location of the black point ( 0.25 meters from each of the right and left charges). The x-component of the net electric field is . The y-component of the net electric field is
A 2.60 N metal bar, (8.75×10^−1)m long and having a resistance of 6.00 Ω, rests horizontally on conducting wires connecting it to the circuit shown in the figure below. The bar is in a uniform, horizontal, 1.60 T magnetic field and is not attached to the wires in the circuit. What is the acceleration of the bar just after the switch S is closed? Express your answer with the appropriate units. Note: Your answer is assumed to be reduced to the highest power possible. Your Answer: x10 Answer units
The density of water at 20∘C and 1 atm pressure is p1 = 998 kg m3. The coefficient of volume expansion at the average temperature of 35∘C is β = 0.337×10−3. The isothermal compressibility of water is given to be α = 4.8×10−5. Consider water initially at 20∘C and 1 atm. Determine the final density of the water with the condition of: a) if it is heated to 50∘C at a constant pressure of 1 atm [20 marks] b) if it is compressed to 100 -atm pressure at a constant temperature of 20∘C. Take the isothermal compressibility of water to be α = 4.8×10−5 atm. [20 marks] (Assumption: The coefficient of volume expansion and the isothermal compressibility of water are constant in the given temperature range. An approximate analysis is performed by replacing differential changes in quantities by finite changes.) [TOTAL: 40 marks]
A conducting rod whose mass and electrical resistance R slides horizontally without friction on conducting strips, as shown in the figure below. Distance between the bars is. A source of about 8 m is connected between the tracks. In the space there prevails a uniform magnetic field B perpendicular to the plane of the figure in an outward direction. Assuming that the rod started its movement from rest, find the a) The direction of movement of the rod. b) EMF induced in a circuit as a function of speed Traffic. c) Rod speed as a function of time. d) The intensity of the current in the rod as a function of time.
Shown in the figure below is a block and track system. All locations indicated by solid black lines are frictionless. The region indicated by the tan hash is a patch of friction with coefficient μk = 0.355. A small block of mass m = 1.37 kg is initially compressed against a spring. The spring constant is k = 90.0 N/m and the initial compression is x1 = 0.3 meters. After the mass leaves the spring it glides down the hill of height y1 = 0.30 meters and eventually slides to a stop after entering the frictional patch. Calculate all the following: The velocity of the mass after it leaves the spring but before it encounters the hill, v2 = m/s The velocity of the mass at the bottom of the hill, v3 = m/s The distance the mass slides onto the frictional area, d = meters
Analyze the free-body diagram, given the coefficients of static and kinetic friction. Determine whether the block will slide and the net force on the system. static μs = 0.25 fs,max = kinetic μk = 0.25 fk N friction is not shown, but must be included in calculations!
A student wants to determine the range of masses that can be hung to keep a block at rest on a table as shown. The coefficient of static friction between the 30 kg box and the surface is 0.3 and the coefficient of kinetic friction is 0.15. What is the smallest mass (m) that will keep the system at rest? In this case, what is strength of the friction? In this case, what direction is the friction? What is the largest mass (m) that will keep the system at rest? In this case, what is strength of the friction? In this case, what direction is the friction?
A curve in a speed track has a radius of 1, 140 ft and a rated speed of 125 mi/h. (Rated speed is speed at which no friction is needed to keep car on road - see hint). Knowing that a racing car starts skidding on the curve when traveling at a speed of 155 mi/h, determine the coefficient of static friction between the tires and the track under the prevailing conditions. (hint, you will need to find the banking angle in order to find the friction coefficient). Answer: 0.2097
A spring with a spring constant of k = 161 N/m is initially compressed by a block a distance d = 0.33 m from its unstretched length. The block is on a horizontal surface with coefficients of static and kinetic friction μs and μk and has a mass of m = 10 kg. Refer to the figure. Part (a) The block is released from the initial position and begins to move to the right. Enter an expression for the sum of the forces in the x-direction in the configuration shown above, in terms of defined quantities and g. Part (b) Calculate the smallest value for the coefficient of static friction μs that would keep the block from moving. Part (c) Assuming the block has just begun to move and the coefficient of kinetic friction is μk = 0.2, what is the block's acceleration in meters per second squared? a =
A 63 kg skier is coasting up the hill shown below with speed vi = 14 m/s. Figure 7.37 The skier's initial kinetic energy is partially used in coasting to the top of a rise. What is the final speed on top of the rise assuming that there is no friction acting? m/s. Instead, assume that friction acts only on the straight line part of the rise and that the coefficient of friction is 0.21. What is the length of the straight line part of the rise? m. What is the normal force acting on skier during the straight line part of the rise? N. What is the final speed on top of the rise assuming that friction acts only during the straight line part? m/s.
A 1-lb collar is attached to a spring and slides without friction along a circular rod in a vertical plane. The spring has an undeformed length of 5 in. and a constant k = 13 lb/ft. Knowing that the collar is released from being held at A determine, the speed of the collar and the normal force between the collar and the rod as the collar passes through B. The speed of the collar and the normal force between the collar and the rod as the collar passes through B is ft/s and Ib respectively.
The drawing shows a skateboarder moving at 5.80 m/s along a horizontal section of a track that is slanted upward by θ = 37.0∘ above the horizontal at its end, which is 0.690 m above the ground. When she leaves the track, she follows the characteristic path of projectile motion. Ignoring friction and air resistance, find the maximum height H to which she rises above the end of the track.
The drawing shows a skateboarder moving at 6.60 m/s along a horizontal section of a track that is slanted upward by θ = 36.0∘ above the horizontal at its end, which is 0.670 m above the ground. When she leaves the track, she follows the characteristic path of projectile motion. Ignoring friction and air resistance, find the maximum height H to which she rises above the end of the track.
A 3 kg toy car sits at the highest point of a 13 m high hill. The car is gently pushed forward until it begins to roll down the slope. Assuming the car coasts freely, without any friction or air resistance, how much kinetic energy (KE) and potential energy (PE) will it have at each of the indicated points? Complete the diagram by placing the correct label in each bin. Use g = 10 m/s2 for he acceleration due to gravity. The diagram is not drawn to scale.
In an exciting game, a baseball player manages to safely slide into second base. The mass of the baseball player is 77.7 kg and the coefficient of kinetic friction between the ground and the player is 0.45 . (a) Find the magnitude of the frictional force in newtons. N (b) It takes the player 1.4 s to come to rest. What was his initial velocity (in m/s )? m/s
(a) A 4.29 kg salami is supported by a cord that runs to a spring scale, which is supported by another cord from the ceiling (see Figure (a)). What is the reading on the scale, which is marked in weight units? (b) In Figure (b) the salami is supported by a cord that runs around a pulley and to a scale. The opposite end of the scale is attached by a cord to a wall. What is the reading on the scale? (c) In Figure (c) the wall has been replaced with a second 4.29 kg salami on the left, and the assembly is stationary. What is the reading on the scale now? (a) (b) Spring scale (c) (a) Number Units
Problem 04.020 - Boundary work for air A piston-cylinder device contains 0.170 kg of air initially at 2 MPa and 350∘C. The air is first expanded isothermally to 500 kPa, then compressed polytropically with a polytropic exponent of 1.2 to the initial pressure, and finally compressed at the constant pressure to the initial state. Determine the boundary work for each process and the network of the cycle. The properties of air are R = 0.287 kJ/kg⋅K and k = 1.4. (Round the final answers to three decimal places. ) (Include a minus sign if necessary. ) The boundary work for the isothermal expansion process is kJ. The boundary work for the polytropic compression process is kJ. The boundary work for the constant pressure compression process is kJ. The network for the cycle is kJ.
A mine car (mass = 450 kg) rolls at a speed of 0.50 m/s on a horizontal track, as the drawing shows. A 110−kg chunk of coal has a speed of 1.2 m/s when it leaves the chute. Determine the speed of the car-coal system after the coal has come to rest in the car. m/s
A mine car (mass = 440 kg) rolls at a speed of 0.50 m/s on a horizontal track, as the drawing shows. A 200−kg chunk of coal has a speed of 0.98 m/s when it leaves the chute. Determine the speed of the car-coal system after the coal has come to rest in the car.
A block of mass m = 2.6 kg is dropped (starting from rest) from a height h = 0.76 meters above the top of an ideal spring with a spring constant of k = 254 newtons per meter. The spring is originally at its equilibrium length (and the mass of the spring is negligible). The block falls on the top of the spring and compresses it a distance d from its equilibrium length before the spring sends it flying back up into the air. Ignore friction and other non-conservative forces, and let g = 9.81 meters per second squared. What is the maximum compression d of the spring (in units of meters)? This one, too. You will need to show your work by submitting your solution for this question.
As shown in the diagram above, a block of mass m slides down a plane inclined at an angle of theta = θ above horizontal. The coefficient of static friction between the block and the plane is mus = μs. The coefficient of kinetic friction between the block and the plane is muk = μk. The block is sliding down the plane. The magnitude of the friction force that the block exerts on the plane must be equal to which of the following? Choose all that apply. More than one answer may be correct. μsmgsin(θ)[ that says musmgsin( theta )] μsmgcos(θ) [ that says musmgcos( theta) ] mgsin(θ) [ that says mgsin( theta) ] mgcos(θ) [ that says mgcos( theta)] μkmgcos(θ) [ that says mukmgcos( theta) ] μkmgsin(θ) [ that says mukmgsin( theta) ]
An elevator car has two equal masses attached to the ceiling as shown. (Assume m = 3.70 kg.) (a) The elevator ascends with an acceleration of magnitude 1.40 m/s2. What are the tensions in the two strings? (Enter your answers in N.) T1 = N T2 = N (b) The maximum tension the strings can withstand is 86.2 N. What is the maximum acceleration of the elevator so that a string does not break? (Enter the magnitude in m/s2.) m/s2
A 6.00 kg block and a 8.00 kg blocks are connected as shown. When released, the 6.00 kg block accelerates downward and the 8.00 kg block accelerates to the right. After each block has moved 2.00 cm, the total work done on the 8.00 kg block. . . . a) is greater than total work done on the 6.00 kg block b) is the same as the total work done on the 6.00 kg block c) is less than the total work done on the 6.00 kg block d) not enough information given to decide
A 6.00 kg block and a 8.00 kg blocks are connected as shown. When released, the 6.00 kg block accelerates downward and the 8.00 kg block accelerates to the right. After each block has moved 2.00 cm, the work done on the 6.00 kg block by tension. . . . a) is negative b) is positive c) is zero d) not enough information given to decide
Use the worked example above to help you solve this problem. At a party, 5.00 kg of ice at −5.20∘C is added to a cooler holding 30 liters of water at 20.0∘C. What is the temperature of the water when it comes to equilibrium? ∘C
What mass of ice at −10.3∘C is needed to cool a whale's water tank, holding 1.18×103 m3 of water, from 20.0∘C down to a more comfortable 10.0∘C? kg
(5) Two blocks of masses M and 4M are placed on a horizontal, frictionless surface. A light spring is attached to one of them, and the blocks are pushed together with the spring between them, as seen in the figure below. A cord initially holding the blocks together is burned; after this the block of mass 4M moves to the right (the positive direction) with a speed of v1 = 2.38 m/s. (a) (b) (5a) What is the velocity of the block of mass M? (5b) Calculate the original elastic energy in the spring if M = 0.375 kg. Submit Answer Tries 0 /10
A force F→1 of magnitude 5.50 units acts on an object at the origin in a direction θ = 54.0∘ above the positive x-axis. (See the figure below. ) A second force F→2 of magnitude 5.00 units acts on the object in the direction of the positive y-axis. Find graphically the magnitude and direction of the resultant force F→1 + F→2. magnitude units direction ० counterclockwise from the +x-axis
The figure here shows an overhead view of three horizontal forces acting on a cargo canister that was initially stationary but that now moves across a frictionless floor. The force magnitudes are F1 = 2.80 N. F2 = 3.90 N and F3 = 10.0 N, and the indicated angles are θ2 = 48.0∘ and θ3 = 34.0∘. What is the net work done on the canister by the three forces during the first 4.30 m of displacement? Number Unit
A trailer truck enters a 2 percent uphill grade traveling at 66 km/h and reaches a speed of 108 km/h in 300 m. The cab has a mass of 1800 kg and the trailer 5400 kg. Determine the average force at the wheels of the cab. The average force at the wheels of the cab is: kN. NOTE: This is a multi-part question. Once an answer is submitted, you will be unable to return to this part.
In the figure, a constant force F→a of magnitude 83.0 N is applied to a 6.0 kg shoe box at angle φ = 57.0∘, causing the box to move up a frictionless ramp at constant speed. How much work is done on the box by F→a when the box has moved through vertical distance h = 0.45 m? Number Units
Particle A of charge 3.50×10−4 C is at the origin, particle B of charge −6.20×10−4 C is at (4.48 m, 0) and particle C of charge 1.10×10−4 C is at (0, 3.88 m). (a) What is the x-component of the electric force exerted by A on C? (b) What is the y-component of the force exerted by A on C? N (c) Find the magnitude of the force exerted by B on C. N (d) Calculate the x-component of the force exerted by B on C. N (e) Calculate the y-component of the force exerted by B on C. N (f) Sum the two x-components to obtain the resultant x-component of the electric force acting on C. N (g) Repeat part (f) for the y-component. N (h) Find the magnitude and direction of the resultant electric force acting on C. magnitude N direction ∘ counterclockwise from the +x-axis
Tom enlists the help of his friend John to move his car. They apply forces to the car as shown in the diagram. Here |F→1| = 423 N, |F→2| = 365 N and friction is negligible. Mass of the car = 3.50×103 kg, θ1 = 12.0∘, and θ2 = 25.0∘. The diagram below shows the top view of the car which is in the x−z plane (horizontal plane). (a) Find the resultant force exerted on the car. (Express your answer in vector notation.) (b) What is the acceleration of the car? (Express your answer in vector notation.) m/s2
A hot-air balloon is rising straight up with a speed of 4.84 m/s. A ballast bag is released from rest relative to the balloon when it is 2.87 m above the ground. How much time elapses before the ballast bag hits the ground? Number Units
The drawing shows a frictionless incline and pulley. The two blocks are connected by a wire (mass per unit length = 0.0330 kg/m) and remain stationary. A transverse wave on the wire has a speed of 70.5 m/s. Neglecting the weight of the wire relative to the tension in the wire, find the masses m1 and m2 of the blocks. (10a) m1: Submit Answer Tries 0 /10 (10b) m2: Submit Answer Tries 0 /10
A car initially traveling eastward turns north by traveling in a circular path at uniform speed as in the figure below. The length of the arc ABC is 214 m, and the car completes the turn in 42.0 s. (a) What is the acceleration when the car is at B located at an angle of 35.0∘? Express your answer in terms of the unit vectors ı and j^. m/s2 ı^ + m/s2 ȷ^ (b) Determine the car's average speed. m/s (c) Determine its average acceleration during the 42.0-s interval. m/s2 ı^ + m/s2 j^
Each of the two systems is released from rest. Calculate the speed v of each 52-lb cylinder after the 42-lb cylinder has dropped 4.2 ft. The 16-lb cylinder of case (a) is replaced by a 16-lb force in case (b). (a) (b) Answers: (a) v = ft/sec (b) v = ft/sec
The coefficients of friction μs = 0.40 and μk = 0.30 between all surfaces of contact. Determine the smallest force p required to start the 30 kg block moving if cable AB is attached as shown, [20 marks] A body of weight 2000 N moves on a level horizontal rough road for a distance of 200 m. The resistance of the road is 10 N per 1000 N weight of the body. Find the work done by the resistance on the body. [05 marks]
A 2.3 kg object moving at an angle of 33 degrees with respect to the x-axis, with a speed 1.5 m/s experiences the force shown. What are the object's speed and direction after the force ends? a) speed: m/s. Give your answer correct to 2 decimal places. b) direction enter your answer in degrees with respect to the x-axis. Give your answer correct to 1 decimal place.
In the figure, a constant force F→a of magnitude 83.0 N is applied to a 6.0 kg shoe box at angle φ = 57.0∘, causing the box to move up a frictionless ramp at constant speed. How much work is done on the box by F→a when the box has moved through vertical distance h = 0.45 m? Number Units
In the instant of the figure, two particles move in an xy plane. Particle P1 has mass 3.63 kg and speed v1 = 8.40 m/s, and it is at distance d1 = 2.25 m from point O (the figure is not drawn to scale). Particle P2 has mass 6.64 kg and speed v2 = 1.92 m/s, and it is at distance d2 = 5.33 m from point O. What is the magnitude of the net angular momentum of the two particles about O? Number Units
Three 7 kg masses are located at points in the xy plane. What is the magnitude of the resultant force (caused by the other two masses) on the mass at the origin? The universal gravitational constant is 6.6726×10−11 N⋅m2/kg2. Answer in units of N.
Consider a conical pendulum with a bob of mass m = 90.0 kg on a string of length L = 10.0 m that makes an angle of θ = 3.00∘ with the vertical. (Consider +ı^ to be towards the center of the circular path and +ȷ^ to be upward.) (i) (a) Determine the horizontal and vertical components of the force exerted by the string on the pendulum. N ı^ + N j^ (b) Determine the radial acceleration of the bob. m/s2
Multiple-Concept Example 7 explores the approach taken in problems such as this one. The blades of a ceiling fan have a radius of 0.357 m and are rotating about a fixed axis with an angular velocity of +1.03 rad/s. When the switch on the fan is turned to a higher speed, the blades acquire an angular acceleration of +2.89 rad/s2. After 0.695 s have elapsed since the switch was reset, what is (a) the total acceleration (in m/s2 ) of a point on the tip of a blade and (b) the angle ϕ between the total acceleration a→ and the centripetal acceleration a→c (See Figure b)? (a) (b)
Whenever two Apollo astronauts were on the surface of the Moon, a third astronaut orbited the Moon. Assume the orbit to be circular and 385 km above the surface of the Moon, where the acceleration due to gravity is 1.13 m/s2. The radius of the Moon is 1.70×106 m. (a) Determine the astronaut's orbital speed. m/s (b) Determine the period of the orbit. s
Concept Simulation 4.1 reviews the concepts that are important in this problem. The speed of a bobsled is increasing, because it has an acceleration of 2.37 m/s2. At a given instant in time, the forces resisting the motion, including kinetic friction and air resistance, total 687 N. The mass of the bobsled and its riders is 286 kg. (a) What is the magnitude of the force propelling the bobsled forward? (b) What is the magnitude of the net force that acts on the bobsled? (a) Number Units (b) Number Units
A jogger travels a route that has two parts. The first is a displacement A→ of 2.90 km due south, and the second involves a displacement B→ that points due east. The resultant displacement A→ + B→ has a magnitude of 3.90 km. (a) What is the magnitude of B→, and (b) what is the direction of A→ + B→ as a positive angle relative to due south? Suppose that A→ − B→ had a magnitude of 3.90 km. (c) What then would be the magnitude of B→, and (d) what is the direction of A→ − B→ relative to due south? (a) Number Units (b) Number Units (c) Number Units (d) Number Units
shows a cube whose sides are 5 cm long. Over the entire left-hand side of the cube is a uniform electric field E1 = 8900 N/C which is entering the cube at an angle θ1 = 15∘ shown. Over the right-hand side is a uniform electric field E2 = 4700 N/C which is leaving the cube at an angle θ2 = 60∘. Everywhere else, the electric field is zero.
Two point charges are lying on the y-axis as in the figure: q1 = −3.40 μC and q2 = +3.40 μC. They are equidistant from the point P, which lies on the x-axis. (a) What is the magnitude of net electric field at P? (b) A small object of charge 90 = 8.40 μC and mass m = 1.25 g is placed at P. When it is released, what is the magnitude of its acceleration? (a) Number Units (b) Number Units
Two small beads having positive charges q1 = 8 q and q2 = q are fixed at the opposite ends of a horizontal insulating rod of length d = 1.55 m. The bead with charge q1 is at the origin. As shown in the figure below, a third small charged bead is free to slide on the rod. At what position x is the third bead in equilibrium? (i) x = m
In the figure, a crate of mass m = 79 kg is pushed at a constant speed up a frictionless ramp (θ = 33∘) by a horizontal force F→. The positive direction of an x-axis is up the ramp, and the positive direction of a y-axis is perpendicular to the ramp. (a) What is the magnitude of F→? (b) What is the magnitude of the normal force on the crate? (a) Number Units (b) Number Units
Steep safety ramps are built beside mountain highways to enable vehicles with defective brakes to stop safely. A truck enters a 750 -ft ramp at a high-speed vO and travels 720 ft in 9 s at constant deceleration before its speed is reduced to vO/2. Assume the same constant deceleration. Determine the additional time required for the truck to stop. (You must provide an answer before moving on to the next part. ) The additional time required for the truck to stop is s. NOTE: This is a multi-part question. Once an answer is submitted, you will be unable to return to this part.
The acceleration of a race car during the first 35 seconds of a road test is modeled as a(t) = 0.022t2 − 1.71t + 22.55 ft/sec2 where t is the number of seconds since the test began. (a) Write the definite integral notation representing the car's speed after the first 35 seconds. a(t) dt (b) Calculate the value of the definite integral in part (a). (Round your answer to one decimal place.) ft/sec
An ultracentrifuge accelerates from rest to 100, 000 rpm in 2.00 min. (a) What is its angular acceleration in rad/s 2? rad/s2 (b) What is the tangential acceleration (in m/s2 ) of a point 11.00 cm from the axis of rotation? m/s2 (c) What is the radial acceleration in m/s2 and multiples of g of this point at full rpm? a in m/s m/s2 a as a multiple of g g
The diagram below shows four charges at the corners of a square of sides d = 1.30 m. Here, q1 = q2 = −q and q3 = 3.0q, where q = 2.30 nC and q3 is located at the origin. What is the force on the fourth charge q4 = 3.50 nC? Assume that the +x axis is directed to the right and the +y axis is directed up. Express your answer in vector form. Do not enter units in your expression. F→ = N
(a) Suppose the coefficient of kinetic friction between m1 and the plane as shown in the figure below is μk = 0.15, and that m1 = m2 = 2.7 kg. As m2 moves down, determine the magnitude of the acceleration of m1 and m2, given θ = 25∘. (b) What smallest value of μk will keep this system from accelerating?
A point charge q1 = 4.10 nC is located at the x-axis at x = 2.00 m, and a second point charge q2 = −6.30 nC is on the y-axis at y = 1.00 m. What is the total electric flux due to these two point charges through a spherical surface centered at the origin and with the following radius? (a) 0.500 m N⋅m2 /C (b) 1.50 m N⋅m2 /C (c) 2.50 m N⋅m2 /C
After a mishap, an 88.7 kg circus performer clings to a trapeze, which is being pulled to the side by another circus artist, as shown here. Calculate the tension (in N) in the first rope, T→1, if the person is momentarily motionless. (Enter the magnitude.) N Calculate the tension (in N) in the second rope, T→2, if the person is momentarily motionless. (Enter the magnitude.) N
When released from rest, a 190 g block slides down the path shown below, reaching the bottom with a speed of 3.8 m/s. How much work does the force of friction do (in J)? J
The displacement (in centimeters) of a particle s moving back and forth along a straight line is given by the equation s = 2 sin(πt) + 4 cos(πt), where t is measured in seconds. (Round your answers to two decimal places. ) (a) Find the average velocity during each time period. (i) [1, 2] cm/s (ii) [1, 1.1] cm/s (iii) [1, 1.01] cm/s (iv) [1, 1.001] cm/s (b) Estimate the instantaneous velocity of the particle when t = 1. cm/s
Suppose you use an ideal pulley of the type shown in the figure below and find it necessary to exert a force of 140 N to support a load. (a) What is the load's mass (in kg )? kg (b) What force (in N) is exerted on the ceiling? Neglect the pulley system's mass. N (upward)
A small sphere of mass m = 7.30 g and charge q1 = 28.7 nC is attached to the end of a string and hangs vertically as in the figure. A second charge of equal mass and charge q2 = −58.0 nC is located below the first charge a distance d = 2.00 cm below the first charge as in the figure. (i) (a) Find the tension in the string. N (b) If the string can withstand a maximum tension of 0.180 N, what is the smallest value d can have before the string breaks? cm
Consider a pulley system of the type shown in the figure above. Suppose that the upper pulley has no mass and the lower two pulleys have a total mass of 7.7 kg; the block attached to the lower pulleys represents a car engine of mass 115 kg. a) What is the tension T in the rope? Assume that all sloped segments of the rope are vertical. N b) What force does the ceiling exert on the upper pulley, assuming you pull straight up on the rope? N If you do not answer this question correctly in 3 attempts, you can get a hint.
Pictured is a thin, nonconducting disk of radius R = 2.92 cm containing an overall charge Q = −50.0 mC, all of which resides on the outside perimeter of the disk and not on the flat surfaces. Determine the potential V at point P located a distance d = 2.65 cm from the disk. Assume that the disk is so thin that its thickness is ignorable. V = V
(a) If the combination is released with the stick horizontal, what is the speed (in m/s) of the center of the disk when the stick is vertical? m/s (b) What is the acceleration (in m/s2) of the center of the disk at the instant the stick is released? (Enter the magnitude.) m/s2 (c) What is the acceleration (in m/s2) of the center of the disk at the instant the stick passes through the vertical? (Enter the magnitude.) m/s2
Starting from rest, a disk rotates about its central axis with constant angular acceleration. In 1.00 s, it rotates 22.8 rad. During that time, what are the magnitudes of (a) the angular acceleration and (b) the average angular velocity? (c) What is the instantaneous angular velocity of the disk at the end of the 1.00 s ? (d) With the angular acceleration unchanged, through what additional angle (rad) will the disk turn during the next 1.00 s? (a) Number Units (b) Number Units (c) Number Units (d) Number Units
An ultracentrifuge accelerates from rest to 100, 000 rpm in 1.40 min. (a) What is its angular acceleration in rad/s2? rad/s2 (b) What is the tangential acceleration, in m/s2, of a point 11.80 cm from the axis of rotation? m/s2 (c) What is the radial acceleration, in m/s2, of this point at full rpm? m/s2 (d) Express this radial acceleration as a multiple of g. g
An ultracentrifuge accelerates from rest to 100, 000 rpm in 1.75 min. (Enter the magnitudes. ) (a) What is the average angular acceleration in rad/s2? rad/s2 (b) What is the tangential acceleration (in m/s2) of a point 9.00 cm from the axis of rotation? m/s2 (c) What is the centripetal acceleration in m/s2 and multiples of g of this point at full rpm? ac in m/s2 m/s2 ac as a multiple of g g (d) What is the total distance traveled (in m) by a point 9.00 cm from the axis of rotation of the ultracentrifuge? m
After a mishap, a 79−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 = 18∘, β = 12∘ and the person is momentarily motionless. You may click the image to enlarge. Help on how to format answers: units. T1 = T2 =
horizontal axis passing through its center as shown in the figure below. The suspended object is released from rest 6.20 m above the floor. (a) Determine the tension in the string (in N). N (b) Determine the magnitude of the acceleration of the object (in m/s2). m/s2 (c) Determine the speed with which the object hits the floor (in m/s). m/s (d) Verify your answer to part (c) by using the isolated system (energy) model. (Submit a file with a maximum size of 1 MB.) Choose File No file chosen
A penny of mass 3.10 g rests on a small 20.0 g block supported by a spinning disk with radius of 12.0 cm. The coefficients of friction between block and disk are 0.850 (static) and 0.590 (kinetic) while those for the penny and block are 0.360 (kinetic) and 0.505 (static). What is the maximum rate of rotation in revolutions per minute that the disk can have, without the block or penny sliding on the disk? rev/min
The acceleration of a particle moving only on a horizontal xy plane is given by a→ = 5ti^ + 6tj^, where a→ is in meters per second-squared and t is in seconds. At t = 0, the position vector r→ = (27.0 m)i^ + (36.0 m)j^ locates the particle, which then has the velocity vector v→ = (7.40 m/s)i^ + (2.20 m/s)j^. At t = 2.80 s, what are (a) its position vector in unit-vector notation and (b) the angle between its direction of travel and the positive direction of the x axis? (a) Number i^ + j^ Units (b) Number Units
Assume the three blocks portrayed in in the figure below move on a frictionless surface and a 42−N force acts as shown on the 3.0-kg block. Determine (a) the acceleration given this system, (b) the tension in the cord connecting the 3.0−kg and the 1.0−kg blocks.
A basketball player is standing on the floor 10.0 m from the basket as shown below. The height of the basket is 3.05 m, and he shoots the ball at a 40.0∘ angle with the horizontal from a height of 2.00 m. (a) What is the acceleration of the basketball at the highest point in its trajectory? (b) How much time does the basketball take to reach the basket?
A point charge with charge q1 = 2.40 μC is held stationary at the origin. A second point charge with charge q2 = −4.60 μC moves from the point ( 0.165 m, 0 ) to the point (0.240 m, 0.275 m ). How much work W is done by the electric force on the moving point charge? Express your answer in joules. Use k = 8.99×109 N⋅m2 /C2 for Coulomb's constant: k = 1 4πϵ0. View Available Hint(s) W = J
A block attached to a spring's position is shown at t = 0. The maximum speed of the block is measured to be 20 m/s. Its spring constant is 0.5 N/m. Write the equation for position as a function of time using the cosine function.
The initially stationary 15−kg block is subjected to the time-varying force whose magnitude P is shown in the plot. Note that the force is zero for all times greater than 3 s. Determine the time ts at which the block comes to rest.
Part A Determine the distance it must be towed by a force F = 4 kN in order to attain a speed of 5 m/s. Neglect friction and the mass of the wheels. Express your answer to three significant figures and include the appropriate units. s =
Two blocks of mass m1 = 3.00 kg and m2 = 6.50 kg are connected by a massless string that passes over a frictionless pulley (Fig. P5.68). The inclines are frictionless. Figure P5.68 (a) Find the magnitude of acceleration of each block. m/s2 (b) Find the tension in the string.
The magnitude of each of these charges is q = 8.60×10−12 C. The lengths of the sides of the rectangles are 3.00 cm and 5.00 cm. (a) Find the magnitude of the electric field at the center of the square. (b) What is the force felt by the charge on at the lower left? (c) Find the electric potential at the center of the rectangle.
A student wants to determine the range of masses that can be hung to keep a block at rest on a table as shown. The coefficient of static friction between the 30 kg box and the surface is 0.3 and the coefficient of kinetic friction is 0.15. What is the smallest mass (m) that will keep the system at rest? In this case, what is strength of the friction? In this case, what direction is the friction? What is the largest mass (m) that will keep the system at rest? In this case, what is strength of the friction? In this case, what direction is the friction?
The height (in meters) of a projectile shot vertically upward from a point 2 m above ground level with an initial velocity of 23.5 m/s is h = 2 + 23.5t − 4.9t2 after t seconds. (a) Find the velocity (in m/s ) after t seconds. v(t) = Find the velocity (in m/s ) after 2 seconds and after 4 seconds. v(2) = m/s v(4) = m/s (b) What is the value (in m/s ) of v(t) when the projectile reaches its maximum height? v(t) = m/s When (in s) does the projectile reach its maximum height? (Round your answer to two decimal places.) s (c) What is the maximum height (in m)? (Round your answer to two decimal places.) m (d) When (in s) does it hit the ground? (Round your answer to two decimal places.) S (e) With what velocity (in m/s ) does it hit the ground? (Round your answer to two decimal places.) m/s
A block (m = 1 kg) slides down an incline plane (θ = 25∘) as shown below. It starts at rest. A. Draw a free body diagram. Include friction. You can draw it on the diagram above. (5 points) B. If you neglect friction, how fast is it going at the bottom? (5 points) C. Considering friction with a coefficient of static friction of μk = 0.1, how fast is the block going at the bottom? (15 points)
Bob and Julie have gone to a park where there is a 5 m, 100 kg see saw (teeter totter), with the fulcrum located at x = 2 m, as shown below. Bob, whose mass is 35 kg, sits at the end on the 'short' side of the see saw (at x = 0), while Julie, whose mass is 20 kg, sits on the end on the 'long' side of the see saw (at x = 3 m). Where should a 30 kg weight be placed, relative to Bob on the x-axis, to make the see saw balance?
A pendulum consists of a rod of length 2 m and mass 7 kg with a solid sphere of mass 3 kg and radius 0.4 m attached at one end. The axis of rotation is as shown below. What is the angular velocity (in rad/s ) of the pendulum at its lowest point if it is released from rest at an angle of 30∘ from the vertical? (Enter the magnitude.) rad/s
Resistance to the motion of an automobile consists of road friction, which is almost independent of speed, and air drag, which is proportional to speed-squared. For a certain car with a weight of 19800 N, the total resistant force F is given by F = 290 + 2.5v2, where F is in newtons and v is in meters per second. Calculate the power required to accelerate the car at 0.68 m/s2 when the speed is 72 km/h. Number Units
Consider the following Velocity vs. Time graph. Which of the following statements are true? Select all that apply. During the first half of the displayed motion, the object is slowing down. The acceleration of the object changes direction at 5 seconds in time. The object is constantly getting faster for the entire duration of the graph. The acceleration of the object is always in a positive direction. For an instant at a time of 5 seconds, the object has stopped moving. For an instant at a time of 5 seconds, the object has zero acceleration.
Three particles with charges q1 = +10 μC, q2 = −20 μC and q3 = +30 μC, are positioned at the vertices of an isosceles triangle with sides a = 0.1 m b = 0.06 m as shown in the Figure. How much work must we do to exchange the positions of q1 and q3? Give your answer in Joules. Hint: What is the Energy of the system of 3 charges as they are and what is its Energy when the positions of q1 and q3 are exchanged? What does the difference between these energies represent? +30 J −30 J +54 J −54 J +24 J −24 J +18 J −18 J +6 J −6 J
A proton accelerates from rest in a uniform electric field of 695 N/C. At one later moment, its speed is 1.15 Mm/s (nonrelativistic because v is much less than the speed of light). (a) Find the acceleration of the proton. (b) Over what time interval does the proton reach this speed? (c) How far does it move in this time interval? (d) What is its kinetic energy at the end of this interval?
A cat runs across the field at a speed of 13 m/s. She is headed Northwest (35∘ West of North) and she jumps off the ground at an angle 60∘ from the ground, as shown in the figures below. The angle her velocity makes with the z axis is 40∘ and the angle the projection of her velocity onto the x-y plane makes with the y axis is 35∘. Write her velocity as a vector using the coordinate system below. ( 10 points)
In the figure below, each charged particle is located at one of the four vertices of a square with side length = a. In the figure, A = 3, B = 4, and C = 3, and q > 0. (i) (a) What is the expression for the magnitude of the electric field in the upper right corner of the square (at the location of q )? (Use the following as necessary: q, a, and ke⋅) E = Give the direction angle (in degrees counterclockwise from the +x-axis) of the electric field at this location. (counterclockwise from the +x-axis) (b) Determine the expression for the total electric force exerted on the charge q. (Enter the magnitude. Use the following as necessary: q, a, and ke. ) F = Give the direction angle (in degrees counterclockwise from the +x-axis) of the electric force on q. ∘ (counterclockwise from the +x-axis) (c) What If? How would the answers to parts (a) and (b) change if each of the four charges were negative with the same magnitude? Select all that apply. The force would be the same magnitude but opposite direction as the force in part (b). The electric field would be the same magnitude and direction as the field in part (a). The force would be the same magnitude and direction as the force in part (b). The electric field would be the same magnitude but opposite direction as the field in part (a).
Consider the 65.0 kg ice skater being pushed by two others shown in the figure. (a) Find the direction (in degrees) and magnitude (in N) of Ftot the total force exerted on her by the others, given that the magnitudes F1 and F2 are 24.8 N and 16.6 N, respectively. direction ∘ (counterclockwise from the direction of F1 is positive) magnitude N (b) What is her initial acceleration (in m/s2) if she is initially stationary and wearing steel-bladed skates that point in the direction of Ftot? (Assume the value of μs for steel on ice is 0.04.) (c) What is her acceleration (in m/s2 ) assuming she is already moving in the direction of Ftot? Remember that friction is always in the opposite direction of motion or attempted motion between surfaces in contact. m/s2 (in the direction of Ftot)