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College Physics 2017

Raymond A. Serway, Chris Vuille, John hughes

Chapter 4

Newton’s Laws of Motion

Educators

AC

Problem 1

The heaviest invertebrate is the giant squid, which is estimated to have a weight of about 2 tons spread out over its length of 70 feet. What is its weight in newtons?

Zulfiqar A.
Numerade Educator

Problem 2

A football punter accelerates a football from rest to a speed of 10 m/s during the time in which his toe is in contact with the ball (about 0.20 s). If the football has a mass of 0.50 kg, what average force does the punter exert on the ball?

Averell H.
Carnegie Mellon University

Problem 3

A 6.0 $\mathrm{kg}$ object undergoes an acceleration of 2.0 $\mathrm{m} / \mathrm{s}^{2}$ .
(a) What is the magnitude of the resultant force acting on it?
(b) If this same force is applied to a 4.0 $\mathrm{kg}$ object, what accel- eration is produced?

Zulfiqar A.
Numerade Educator

Problem 4

One or more external forces are exerted on each object enclosed in a dashed box shown in Figure 4.2. Identify the reaction to each of these forces.

Averell H.
Carnegie Mellon University

Problem 5

A bag of sugar weighs 5.00 lb on Earth. What would it weigh in newtons on the Moon, where the free-fall acceleration is one-sixth that on Earth? Repeat for Jupiter, where g is 2.64 times that on Earth. Find the mass of the bag of sugar in kilograms at each of the three locations.

Zulfiqar A.
Numerade Educator

Problem 6

A freight train has a mass of $1.5 \times 10^{7} \mathrm{kg} .$ If the locomotive can exert a constant pull of $7.5 \times 10^{5} \mathrm{N}$ , how long does it take to increase the speed of the train from rest to 80 $\mathrm{km} / \mathrm{h}$ ?

Averell H.
Carnegie Mellon University

Problem 7

Four forces act on an object, given by $\overrightarrow{\mathbf{A}}=40.0 \mathrm{N}$ east, $\overrightarrow{\mathbf{B}}=50.0$ north, $\overrightarrow{\mathbf{C}}=70.0 \mathrm{N}$ west, and $\overrightarrow{\mathbf{D}}=90.0 \mathrm{N}$ south. (a) What is the magnitude of the net force on the object? (b) What is the direction of the force?

Zulfiqar A.
Numerade Educator

Problem 8

Consider a solid metal sphere (S) a few centimeters in diameter and a feather (F). For each quantity in the list that follows, indicate whether the quantity is the same, greater, or lesser in the case of S or in that of F. Explain in each case why you gave the answer you did. Here is the list: (a) the gravitational force, (b) the time it will take to fall a given distance in air, (c) the time it will take to fall a given distance in vacuum, (d) the total force on the object when falling in vacuum.

Averell H.
Carnegie Mellon University

Problem 9

As a fish jumps vertically out of the water, assume that only two significant forces act on it: an upward force F exerted by the tail fin and the downward force due to gravity. A record Chinook salmon has a length of 1.50 m and a mass of 61.0 kg. If this fish is moving upward at 3.00 m/s as its head first breaks the surface and has an upward speed of 6.00 m/s after two- thirds of its length has left the surface, assume constant acceleration and determine (a) the salmon’s acceleration and (b) the magnitude of the force F during this interval.

Zulfiqar A.
Numerade Educator

Problem 10

A 5.0-g bullet leaves the muzzle of a rifle with a speed of 320 m/s. What force (assumed constant) is exerted on the bullet while it is traveling down the 0.82-m-long barrel of the rifle?

Averell H.
Carnegie Mellon University

Problem 11

A boat moves through the water with two forces acting on it. One is a $2.00 \times 10^{3}-\mathrm{N}$ forward push by the water on the propeller, and the other is a $1.80 \times 10^{3}-\mathrm{N}$ resistive force due to the water around the bow. (a) What is the acceleration of the $1.00 \times 10^{3}-\mathrm{kg}$ boat? (b) If it starts from rest, how far will the boat move in 10.0 s? (c) What will its velocity be at the end of that time?

Zulfiqar A.
Numerade Educator

Problem 12

Two forces are applied to a car in an effort to move it, as shown in Figure P4.12.
(a) What is the resultant vector of these two forces?
(b) If the car has a mass of 3 000 kg, what acceleration does it have? Ignore friction.

Averell H.
Carnegie Mellon University

Problem 13

A 970.-kg car starts from rest on a horizontal roadway and accelerates eastward for 5.00 s when it reaches a speed of 25.0 m/s. What is the average force exerted on the car during this time?

Zulfiqar A.
Numerade Educator

Problem 14

An object of mass m is dropped from the roof of a building of height h. While the object is falling, a wind blowing parallel to the face of the building exerts a constant horizontal force F on the object. (a) How long does it take the object to strike the ground? Express the time t in terms of g and h. (b) Find an expression in terms of m and F for the acceleration ax of the object in the horizontal direction (taken as the positive x - direction). (c) How far is the object displaced horizontally before hitting the ground? Answer in terms of m, g, F, and h. (d) Find the magnitude of the object’s acceleration while it is falling, using the variables F, m, and g.

Averell H.
Carnegie Mellon University

Problem 15

After falling from rest from a height of 30.0 m, a 0.500-kg ball rebounds upward, reaching a height of 20.0 m. If the contact between ball and ground lasted 2.00 ms, what average force was exerted on the ball?

Zulfiqar A.
Numerade Educator

Problem 16

The force exerted by the wind on the sails of a sailboat is 390 N north. The water exerts a force of 180 N east. If the boat (including its crew) has a mass of 270 kg, what are the magnitude and direction of its acceleration?

Averell H.
Carnegie Mellon University

Problem 17

A force of 30.0 N is applied in the positive x - direction to a block of mass 8.00 kg, at rest on a frictionless surface. (a) What is the block’s acceleration? (b) How fast is it going after 6.00 s?

Zulfiqar A.
Numerade Educator

Problem 18

What would be the acceleration of gravity at the surface of a world with twice Earth’s mass and twice its radius?

Averell H.
Carnegie Mellon University

Problem 19

Calculate the magnitude of the normal force on a 15.0-kg block in the following circumstances: (a) The block is resting on a level surface. (b) The block is resting on a surface tilted up at a $30.0^{\circ}$ angle with respect to the horizontal. (c) The block is resting on the floor of an elevator that is accelerating upwards at 3.00 $\mathrm{m} / \mathrm{s}^{2} .(\mathrm{d})$ The block is on a level surface and a force of 125 $\mathrm{N}$ is exerted on it at an angle of $30.0^{\circ}$ above the horizontal.

Zulfiqar A.
Numerade Educator

Problem 20

A horizontal force of 95.0 $\mathrm{N}$ is applied to a 60.0 $\mathrm{kg}$ crate on a rough, level surface. If the crate accelerates at 1.20 $\mathrm{m} / \mathrm{s}^{2}$ , what is the magnitude of the force of kinetic friction acting on the crate?

Averell H.
Carnegie Mellon University

Problem 21

A car of mass 875 kg is traveling 30.0 m/s when the driver applies the brakes, which lock the wheels. The car skids for 5.60 s in the positive x - direction before coming to rest. (a) What is the car’s acceleration? (b) What magnitude force acted on the car during this time? (c) How far did the car travel?

Zulfiqar A.
Numerade Educator

Problem 22

A student of mass 60.0 $\mathrm{kg}$ , starting at rest, slides down a slide 20.0 $\mathrm{m}$ long, tilted at an angle of $30.0^{\circ}$ with respect to the horizontal. If the coefficient of kinetic friction between the student and the slide is $0.120,$ find ( a) the force of kinetic friction, (b) the acceleration, and (c) the speed she is traveling when she reaches the bottom of the slide.

Averell H.
Carnegie Mellon University

Problem 23

A $1.00 \times 10^{3}-\mathrm{N}$ crate is being pushed across a level floor at a constant speed by a force $\overrightarrow{\mathbf{F}}$ of $3.00 \times 10^{2} \mathrm{N}$ at an angle of $20.0^{\circ}$ below the horizontal, as shown in Figure P4.23a. (a) What is the coefficient of kinetic friction between the crate and the floor? (b) If the $3.00 \times 10^{2}-\mathrm{N}$ force is instead pulling the block at an angle of $20.0^{\circ}$ above the horizontal, as shown in Figure P4.23b, what will be the acceleration of the crate? Assume that the coefficient of friction is the same as that found in part (a).

Zulfiqar A.
Numerade Educator

Problem 24

A block of mass $m=5.8 \mathrm{kg}$ is pulled up a $\theta=25^{\circ}$ incline as in Figure $\mathrm{P} 4.24$ with a force of magnitude $F=32 \mathrm{N}$ . (a) Find the acceleration of the block if the incline is frictionless. (b) Find the acceleration of the block if the coefficient of kinetic friction between the block and incline is 0.10.

Averell H.
Carnegie Mellon University

Problem 25

A rocket takes off from Earth's surface, accelerating straight up at 72.0 $\mathrm{m} / \mathrm{s}^{2}$ . Calculate the normal force acting on an astronaut of mass $85.0 \mathrm{kg},$ including his space suit.

Zulfiqar A.
Numerade Educator

Problem 26

A man exerts a horizontal force of 125 N on a crate with a mass of 30.0 kg. (a) If the crate doesn’t move, what’s the magnitude of the static friction force? (b) What is the minimum possible value of the coefficient of static friction between the crate and the floor?

Averell H.
Carnegie Mellon University

Problem 27

A horse is harnessed to a sled having a mass of $236 \mathrm{kg},$ includ- ing supplies. The horse must exert a force exceeding 1240 $\mathrm{N}$ at an angle of $35.0^{\circ}$ in order to get the sled moving. Treat the sled as a point particle. (a) Calculate the normal force on the sled when the magnitude of the applied force is 1 240 N. (b) Find the coefficient of static friction between the sled and the ground beneath it. (c) Find the static friction force when the horse is exerting a force of $6.20 \times 10^{2} \mathrm{N}$ on the sled at the same angle.

Zulfiqar A.
Numerade Educator

Problem 28

A block of mass 55.0 kg rests on a slope having an angle of elevation of $25.0^{\circ} .$ If pushing downhill on the block with a force just exceeding 187 $\mathrm{N}$ and parallel to the slope is sufficient to cause the block to start moving, find the coefficient of static friction.

Averell H.
Carnegie Mellon University

Problem 29

A dockworker loading crates on a ship finds that a 20.0-kg crate, initially at rest on a horizontal surface, requires a 75.0-N horizontal force to set it in motion. However, after the crate is in motion, a horizontal force of 60.0 N is required to keep it moving with a constant speed. Find the coefficients of static and kinetic friction between crate and floor.

Zulfiqar A.
Numerade Educator

Problem 30

Suppose the coefficient of static friction between a quarter and the back wall of a rocket car is 0.330. At what minimum rate would the car have to accelerate so that a quarter placed on the back wall would remain in place?

Averell H.
Carnegie Mellon University

Problem 31

The coefficient of static friction between the 3.00-kg crate and the $35.0^{\circ}$ incline
of Figure $P 4.31$ is 0.300 , What minimum force $\overline{\mathbf{F}}$ must be applied to the crate perpendicular to the incline to prevent the crate from sliding down the incline?

Zulfiqar A.
Numerade Educator

Problem 32

Two identical strings making an angle of $\theta=30.0^{\circ}$ with respect to the vertical support a block of mass $m=15.0 \mathrm{kg}$ (Fig. P4.32). What is the tension in each of the strings?

Averell H.
Carnegie Mellon University

Problem 33

A $75-\mathrm{kg}$ man standing on a scale in an elevator notes that as the elevator rises, the scale reads 825 $\mathrm{N}$ . What is the acceleration of the elevator?

Zulfiqar A.
Numerade Educator

Problem 34

A crate of mass $m=32 \mathrm{kg}$ rides on the bed of a truck attached by a cord to the back of the cab as in Figure P4.34. The cord can with stand a maximum tension of 68 N before breaking. Neglecting friction between the crate and truck bed, find the maximum acceleration the truck can have before the cord breaks.

Averell H.
Carnegie Mellon University

Problem 35

(a) Find the tension in each cable supporting the $6.00 \times 10^{2}-\mathrm{N}$ cat burglar in Figure $\mathrm{P} 4.35 .$ (b) Suppose the horizontal cable were reattached higher up on the wall. Would the tension in the other cables increase, decrease, or stay the same? Why?

Zulfiqar A.
Numerade Educator

Problem 36

The distance between two telephone poles is 50.0 m. When a 1.00-kg bird lands on the telephone wire midway between the poles, the wire sags 0.200 m. Draw a free-body diagram of the bird. How much tension does the bird produce in the wire? Ignore the weight of the wire.

Averell H.
Carnegie Mellon University

Problem 37

(a) An elevator of mass m moving upward has two forces acting on it: the upward force of tension in the cable and the downward force due to gravity. When the elevator is accelerating upward, which is greater, T or w? (b) When the elevator is moving at a constant velocity upward, which is greater, T or w? (c) When the elevator is moving upward, but the acceleration is downward, which is greater, T or w? (d) Let the elevator have a mass of 1 500 kg and an upward acceleration of 2.5 $\mathrm{m} / \mathrm{s}^{2} .$ Find $T .$ Is your answer consistent with the answer to part (a)? (e) The elevator of part (d) now moves with a constant upward velocity of 10 m/s. Find T. Is your answer consistent with your answer to part (b)? (f) Having initially moved upward with a constant velocity, the elevator begins to accelerate downward at 1.50 $\mathrm{m} / \mathrm{s}^{2}$ . Find $T$ . Is your answer consistent with your answer to part ( $(\mathrm{c})$ ?

Zulfiqar A.
Numerade Educator

Problem 38

A certain orthodontist uses a wire brace to align a patient’s crooked tooth as in Figure P4.38. The tension in the wire is adjusted to have a magnitude of 18.0 N. Find the magnitude of the net force exerted by the wire on the crooked tooth.

Averell H.
Carnegie Mellon University

Problem 39

A 150-N bird feeder is supported by three cables as shown in Figure P4.39. Find the tension in each cable.

Zulfiqar A.
Numerade Educator

Problem 40

The leg and cast in Figure P4.40 weigh 220 $\mathrm{N}\left(w_{1}\right)$ . Determine the weight $w_{2}$ and the angle $\alpha$ needed so that no force is exerted on the hip joint by the leg plus the cast.

Averell H.
Carnegie Mellon University

Problem 41

A 276-kg glider is being pulled by a 1 950-kg jet along a horizontal runway with an acceleration of $\overrightarrow{\mathbf{a}}=2.20 \mathrm{m} / \mathrm{s}^{2}$ to the right as in Figure $\mathrm{P} 4.41 .$ Find (a) the thrust provided by the jet's engines and (b) the magnitude of the tension in the cable connecting the jet and glider.

Zulfiqar A.
Numerade Educator

Problem 42

A crate of mass 45.0 kg is being transported on the flatbed of a pickup truck. The coefficient of static friction between the crate and the truck’s flatbed is 0.350, and the coefficient of kinetic friction is 0.320. (a) The truck accelerates forward on level ground. What is the maximum acceleration the truck can have so that the crate does not slide relative to the truck’s flatbed? (b) The truck barely exceeds this acceleration and then moves with constant acceleration, with the crate sliding along its bed. What is the acceleration of the crate relative to the ground?

Averell H.
Carnegie Mellon University

Problem 43

Consider a large truck carrying a heavy load, such as steel beams. A significant hazard for the driver is that the load may slide forward, crushing the cab, if the truck stops suddenly in an accident or even in braking. Assume, for example, a 10 000-kg load sits on the flatbed of a 20 000-kg truck moving at 12.0 m/s. Assume the load is not tied down to the truck and has a coefficient of static friction of 0.500 with the truck bed. (a) Calculate the minimum stopping distance for which the load will not slide forward relative to the truck. (b) Is any piece of data unnecessary for the solution?

Zulfiqar A.
Numerade Educator

Problem 44

A student decides to move a box of books into her dormitory room by pulling on a rope attached to the box. She pulls with a force of 80.0 $\mathrm{N}$ at an angle of $25.0^{\circ}$ above the horizontal. The box has a mass of 25.0 kg, and the coefficient of kinetic friction between box and floor is 0.300. (a) Find the acceleration of the box. (b) The student now starts moving the box up a $10.0^{\circ}$ incline, keeping her 80.0 $\mathrm{N}$ force directed at $25.0^{\circ}$ above the line of the incline. If the coefficient of friction is unchanged, what is the new acceleration of the box?

Khoobchandra A.
Numerade Educator

Problem 45

An object falling under the pull of gravity is acted upon by a frictional force of air resistance. The magnitude of this force is approximately proportional to the speed of the object, which can be written as $f=b v .$ Assume $b=15 \mathrm{kg} / \mathrm{s}$ and $m=$ 50 $\mathrm{kg}$ . (a) What is the terminal speed the object reaches while falling? (b) Does your answer to part (a) depend on the initial speed of the object? Explain.

Zulfiqar A.
Numerade Educator

Problem 46

A $3.00-\mathrm{kg}$ block starts from rest at the top of a $30.0^{\circ}$ incline and slides 2.00 $\mathrm{m}$ down the incline in 1.50 $\mathrm{s}$ . Find $(\mathrm{a})$ the acceleration of the block, (b) the coefficient of kinetic friction between the block and the incline, (c) the frictional force acting on the block, and (d) the speed of the block after it has slid 2.00 $\mathrm{m} .$

Averell H.
Carnegie Mellon University

Problem 47

To meet a U.S. Postal Service requirement, employees’ footwear must have a coefficient of static friction of 0.500 or more on a specified tile surface. A typical athletic shoe has a coefficient of 0.800. In an emergency, what is the minimum time interval in which a person starting from rest can move 3.00 m on the tile surface if she is wearing (a) footwear meeting the Postal Service minimum and (b) a typical athletic shoe?

Zulfiqar A.
Numerade Educator

Problem 48

A block of mass 12.0 kg is sliding at an initial velocity of 8.00 m/s in the positive x - direction. The surface has a coefficient of kinetic friction of 0.300. (a) What is the force of kinetic friction acting on the block? (b) What is the block’s acceleration? (c) How far will it slide before coming to rest?

Averell H.
Carnegie Mellon University

Problem 49

The person in Figure P4.49 weighs 170. lb. Each crutch makes an angle of $22.0^{\circ}$ with the vertical (as seen from the front). Half of the person's weight is supported by the crutches, the other half by the vertical forces exerted by the ground on his feet. Assuming he is at rest and the force exerted by the ground on the crutches acts along the crutches, determine (a) the smallest possible coefficient of friction between crutches and ground and (b) the magnitude of the compression force supported by each crutch.

Maria Gabriela C.
Numerade Educator

Problem 50

A car is traveling at 50.0 km/h on a flat highway. (a) If the coefficient of friction between road and tires on a rainy day is 0.100, what is the minimum distance in which the car will stop? (b) What is the stopping distance when the surface is dry and the coefficient of friction is 0.600?

Averell H.
Carnegie Mellon University

Problem 51

A 5.0-kg bucket of water is raised from a well by a rope. If the upward acceleration of the bucket is $3.0 \mathrm{m} / \mathrm{s}^{2},$ find the force exerted by the rope on the bucket.

Zulfiqar A.
Numerade Educator

Problem 52

A hockey puck struck by a hockey stick is given an initial speed $v_{0}$ in the positive $x$ -direction. The coefficient of kinetic friction between the ice and the puck is $\mu_{k}$ (a) Obtain an expression for the acceleration of the puck. (b) Use the result of part (a) to obtain an expression for the distance $d$ the puck slides. The answer should be in terms of the variables $v_{0}, \mu_{k}$ and $g$ only.

Averell H.
Carnegie Mellon University

Problem 53

A setup similar to the one shown in Figure P4.53 is often used in hospitals to support and apply a traction force to an injured leg. (a) Determine the force of tension in the rope supporting the leg. (b) What is the traction force exerted on the leg? Assume the traction force is horizontal.

Zulfiqar A.
Numerade Educator

Problem 54

An Atwood’s machine (Fig. 4.38) consists of two masses: one of mass 3.00 kg and the other of mass 8.00 kg. When released from rest, what is the acceleration of the system?

Averell H.
Carnegie Mellon University

Problem 55

A block of mass $m_{1}=16.0 \mathrm{kg}$ is on a frictionless table to the left of a second block of mass $m_{2}=24.0 \mathrm{kg}$ , attached by a horizontal string (Fig. P4.55). If a horizontal force of $1.20 \times 10^{2} \mathrm{N}$ is exerted on the block $m_{2}$ in the positive $x$ -direction, (a) use the system approach to find the acceleration of the two blocks. (b) What is the tension in the string connecting the blocks?

Zulfiqar A.
Numerade Educator

Problem 56

Two blocks each of mass m are fastened to the top of an elevator as in Fig- ure P4.56. The elevator has an upward acceleration a. The strings have negligible mass. (a) Find the tensions $T_{1}$ and $T_{2}$ in the upper and lower strings in terms of $m, a,$ and $g$ . (b) Compare the two tensions and determine which string would break first if $a$ is made sufficiently large. (c) What are the tensions if the cable supporting the elevator breaks?

Averell H.
Carnegie Mellon University

Problem 57

Two blocks of masses m and 2m are held in equilibrium on a frictionless incline as in Figure P4.57. In terms of $m$ and $\theta,$ find (a) the magnitude of the tension $T_{1}$ in the upper cord and (b) the magnitude of the tension $T_{2}$ in the lower cord connecting the two blocks.

Zulfiqar A.
Numerade Educator

Problem 58

The systems shown in Figure P4.58 are in equilibrium. If the spring scales are calibrated in newtons, what do they read? Ignore the masses of the pulleys and strings and assume the pulleys and the incline in Figure P4.58d are frictionless.

Averell H.
Carnegie Mellon University

Problem 59

Assume the three blocks portrayed in Figure P4.59 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 the1.0-kg blocks, and (c) the force exerted by the 1.0-kg block on the 2.0-kg block.

Zulfiqar A.
Numerade Educator

Problem 60

Two packing crates of masses 10.0 kg and 5.00 kg are connected by a light string that passes over a frictionless pulley as in Figure P4.60. The 5.00-kg crate lies on a smooth incline of angle 40.0°. Find (a) the acceleration of the 5.00-kg crate and (b) the tension in the string.

Averell H.
Carnegie Mellon University

Problem 61

A $1.00 \times 10^{3}$ car is pulling a $300 .$ -kg trailer. Together, the car and trailer have an acceleration of 2.15 $\mathrm{m} / \mathrm{s}^{2}$ in the positive $x$ -direction. Neglecting frictional forces on the trailer, determine (a) the net force on the car,(b) the net force on the trailer, (c) the magnitude and direction of the force exerted by the trailer on the car, and (d) the resultant force exerted by the car on the road.

Zulfiqar A.
Numerade Educator

Problem 62

Two blocks of masses $m_{1}$ and $m_{2}$ $\left(m_{1}>m_{2}\right)$ are placed on a friction- less table in contact with each other. A horizontal force of magnitude $F$ is applied to the block of mass $m_{1}$ in Figure $\mathrm{P} 4.62 .$ (a) If $P$ is the magnitude of the contact force between the blocks, draw the free-body diagrams for each block. (b) What is the net force on the system consisting of both blocks? (c) What is the net force acting on $m_{1} ?(\mathrm{d})$ What is the net force acting on $m_{2} ?$ (e) Write the $x$ -component of Newton's second law for each block. (f) Solve the resulting system of two equations and two unknowns, expressing the acceleration $a$ and contact force $P$ in terms of the masses and force. (g) How would the answers change if the force had been applied to $m_{2}$ instead? (Hint: use symmetry; don't calculate!) Is the contact force larger, smaller, or the same in this case? Why?

Averell H.
Carnegie Mellon University

Problem 63

In Figure P4.63, the light, taut, unstretchable cord B joins block 1 and the larger-mass block 2. Cord A exerts a force on block 1 to make it accelerate forward. (a) How does the magnitude of the force exerted by cord A on block 1 compare with the magnitude of the force exerted by cord B on block 2? (b) How does the acceleration of block 1 compare with the acceleration of block 2? (c) Does cord B exert a force on block 1? Explain your answer.

Zulfiqar A.
Numerade Educator

Problem 64

An object with mass $m_{1}=5.00 \mathrm{kg}$ rests on a frictionless horizontal table and is connected to a cable that passes over a pulley and is then fastened to a hanging object with mass $m_{2}=10.0 \mathrm{kg}$ , as shown in Figure $\mathrm{P} 4.64 .$ Find $(\mathrm{a})$ the acceleration of each object and (b) the tension in the cable.

Averell H.
Carnegie Mellon University

Problem 65

Objects with masses $m_{1}=10.0 \mathrm{kg}$ and $m_{2}=5.00 \mathrm{kg}$ are connected by a light string that passes over a frictionless pulley as in Figure $P 4.64 .$ If, when the system starts from rest, $m_{2}$ falls 1.00 $\mathrm{m}$ in 1.20 $\mathrm{s}$ , determine the coefficient of kinetic friction between $m_{1}$ and the table

Zulfiqar A.
Numerade Educator

Problem 66

Two objects with masses of 3.00 kg and 5.00 kg are connected by a light string that passes over a frictionless pulley, as in Figure P4.66. Determine (a) the tension in the string, (b) the acceleration of each object, and (c) the distance each object will move in the first second of motion if both objects start from rest.

Averell H.
Carnegie Mellon University

Problem 67

In Figure $\mathrm{P} 4.64, m_{1}=10 . \mathrm{kg}$ and $m_{2}=4.0 \mathrm{kg}$ . The coefficient of static friction between $m_{1}$ and the horizontal surface is $0.50,$ and the coefficient of kinetic friction is $0.30 .(\mathrm{a})$ If the system is released from rest, what will its acceleration be? If the system is set in motion with $m_{2}$ moving downward, what will be the acceleration of the system?

Zulfiqar A.
Numerade Educator

Problem 68

A block of mass 3$m$ is placed on a frictionless horizontal surface, and a second block of mass $m$ is placed on top of the first block. The surfaces of the blocks are rough. A constant force of magnitude $F$ is applied to the first block as in Figure $\mathrm{P} 4.68$ . (a) Construct free- body diagrams for each block. (b) Identify the horizontal force that causes the block of mass $m$ to accelerate. (c) Assume that the upper block does not slip on the lower block, and find the acceleration of each block in terms of $m$ and $F$

Averell H.
Carnegie Mellon University

Problem 69

A 15.0-lb block rests on a horizontal floor. (a) What force does the floor exert on the block? (b) A rope is tied to the block and is run vertically over a pulley. The other end is attached to a free-hanging 10.0-lb object. What now is the force exerted by the floor on the 15.0-lb block? (c) If the 10.0-lb object in part (b) is replaced with a 20.0-lb object, what is the force exerted by the floor on the 15.0-lb block?

Zulfiqar A.
Numerade Educator

Problem 70

Objects of masses $m_{1}=4.00 \mathrm{kg}$ and $m_{2}=9.00 \mathrm{kg}$ are connected by a light string that passes over a frictionless pulley as in Figure $\mathrm{P} 4.70 .$ The object $m_{1}$ is held at rest on the floor, and $m_{2}$ rests on a fixed incline of $\theta=40.0^{\circ} .$ The objects are released from rest, and $m_{2}$ slides 1.00 $\mathrm{m}$ down the incline in 4.00 s. Determine (a) the acceleration of each object, (b) the tension in the string, and (c) the coefficient of kinetic friction between $m_{2}$ and the incline.

Averell H.
Carnegie Mellon University

Problem 71

As a protest against the umpire’s calls, a baseball pitcher throws a ball straight up into the air at a speed of 20.0 m/s. In the process, he moves his hand through a distance of 1.50 m. If the ball has a mass of 0.150 kg, find the force he exerts on the ball to give it this upward speed.

Zulfiqar A.
Numerade Educator

Problem 72

Two blocks each of mass $m=3.50 \mathrm{kg}$ are fastened to the top of an elevator as in Figure $P 4.56 .$ (a) If the elevator has an upward acceleration $a=1.60 \mathrm{m} / \mathrm{s}^{2}$ , find the tensions $T_{1}$ and $T_{2}$ in the upper and lower strings. (b) If the strings can with- stand a maximum tension of $85.0 \mathrm{N},$ what maximum acceleration can the elevator have before the upper string breaks?

Averell H.
Carnegie Mellon University

Problem 73

T h r e e objects are connected on a table as shown in Figure P4.73. The coefficient of kinetic friction between the block of mass $m_{2}$ and the table is 0.350 . The objects have masses of $m_{1}=4.00 \mathrm{kg}, m_{2}=1.00 \mathrm{kg},$ and $m_{3}=2.00 \mathrm{kg}$ as shown, and the pulleys are frictionless. (a) Draw a diagram of the forces on each object. (b) Determine the acceleration of each object, including its direction. (c) Determine the tensions in the two cords. (d) If the tabletop were smooth, would the tensions increase, decrease, or remain the same? Explain.

Zulfiqar A.
Numerade Educator

Problem 74

(a) What is the minimum force of friction required to hold the system of Figure P4.74 in equilibrium? (b) What coefficient of static friction between the 100.-N block and the table ensures equilibrium? (c) If the coefficient of kinetic friction between the 100.-N block and the table is 0.250, what hanging weight should replace the 50.0-N weight to allow the system to move at a constant speed once it is set in motion?

Averell H.
Carnegie Mellon University

Problem 75

(a) What is the resultant force exerted by the two cables supporting the traffic light in Figure P4.75? (b) What is the weight of the light?

Zulfiqar A.
Numerade Educator

Problem 76

A woman at an airport is towing her 20.0-kg suitcase at constant speed by pulling on a strap at an angle $\theta$ above the horizontal (Fig. 4.76$) .$ She pulls on the strap with a $35.0-\mathrm{N}$ force, and the friction force on the suitcase is 20.0 $\mathrm{N}$ . (a) Draw a free-body dia- gram of the suitcase. (b) What angle does the strap make with the horizontal? (c) What is the magnitude of the normal force that the ground exerts on the suitcase?

Averell H.
Carnegie Mellon University

Problem 77

A boy coasts down a hill on a sled, reaching a level surface at the bottom with a speed of 7.00 m/s. If the coefficient of friction between the sled’s runners and the snow is 0.050 0 and the boy and sled together weigh 600. N, how far does the sled travel on the level surface before coming to rest?

Zulfiqar A.
Numerade Educator

Problem 78

Three objects are connected by light strings as shown in Figure P4.78. The string connecting the 4.00-kg object and the 5.00-kg object passes over a light friction-less pulley. Determine (a) the acceleration of each object and (b) the tension in the two strings.

Averell H.
Carnegie Mellon University

Problem 79

A box rests on the back of a truck. The coefficient of static friction between the box and the bed of the truck is 0.300. (a) When the truck accelerates forward, what force accelerates the box? (b) Find the maximum acceleration the truck can have before the box slides.

Zulfiqar A.
Numerade Educator

Problem 80

A high diver of mass 70.0 kg steps off a board 10.0 m above the water and falls vertical to the water, starting from rest. If her downward motion is stopped 2.00 s after her feet first touch the water, what average upward force did the water exert on her?

Averell H.
Carnegie Mellon University

Problem 81

A frictionless plane is 10.0 $\mathrm{m}$ long and inclined at $35.0^{\circ} .$ A sled starts at the bottom with an initial speed of 5.00 $\mathrm{m} / \mathrm{s}$ up the incline. When the sled reaches the point at which it momentarily stops, a second sled is released from the top of the incline with an initial speed $v_{i}$ . Both sleds reach the bottom of the incline at the same moment. (a) Determine the distance that the first sled traveled up the incline. (b) Determine the initial speed of the second sled.

Zulfiqar A.
Numerade Educator

Problem 82

Measuring coefficients of friction A coin is placed near one edge of a book lying on a table, and that edge of the book is lifted until the coin just slips down the incline as shown in Figure P4.82. The angle of the incline, $\theta_{c},$ called the critical angle, is measured. (a) Draw a free-body diagram for the coin when it is on the verge of slipping and identify all forces acting on it. Your free-body diagram should include a force of static friction acting up the incline. (b) Is the magnitude of the friction force equal to $\mu_{s} n$ for angles less than $\theta_{c} ?$ Explain. What can you definitely say about the magnitude of the friction force for any angle $\theta \leq \theta$ ? (c) Show that the coefficient of static friction is given by $\mu_{s}=\tan \theta_{c} \cdot(\mathrm{d})$ Once the coin starts to slide down the incline, the angle can be adjusted to a new value $\theta_{c}^{\prime} \leq \theta_{c}$ such that the coin moves down the incline with constant speed. How does observation enable you to obtain the coefficient of kinetic friction?

Khoobchandra A.
Numerade Educator

Problem 83

A 2.00-kg aluminum block and a 6.00-kg copper block are connected by a light string over a frictionless pulley. The two blocks are allowed to move on a fixed steel block wedge (of angle $\theta=30.0^{\circ}$ ) as shown in Figure P4.83. Making use of Table $4.2,$ determine (a) the acceleration of the two blocks and (b) the tension in the string.

Zulfiqar A.
Numerade Educator

Problem 84

On an airplane’s takeoff, the combined action of the air around the engines and wings of an airplane exerts an 8 000-N force on the plane, directed upward at an angle of $65.0^{\circ}$ above the horizontal. The plane rises with constant velocity in the vertical direction while continuing to accelerate in the horizontal direction. (a) What is the weight of the plane? (b) What is its horizontal acceleration?

Averell H.
Carnegie Mellon University

Problem 85

Two boxes of fruit on a frictionless horizontal surface are connected by a light string as in Figure $\mathrm{P} 4.85,$ where $m_{1}=10.0 \mathrm{~kg}$ and $m_{2}=20.0 \mathrm{~kg} .$ A force of $50.0 \mathrm{~N}$ is applied to the $20.0-\mathrm{kg}$ box. (a) Determine the acceleration of each box and the tension in the string. (b) Repeat the problem for the case where the coefficient of kinetic friction between each box and the surface is 0.10 .

Zulfiqar A.
Numerade Educator

Problem 86

A sled weighing 60.0 N is pulled horizontally across snow so that the coefficient of kinetic friction between sled and snow is 0.100. A penguin weighing 70.0 N rides on the sled, as in Figure P4.86. If the coefficient of static friction between penguin and sled is 0.700, find the maximum horizontal force that can be exerted on the sled before the penguin begins to slide off.

Averell H.
Carnegie Mellon University

Problem 87

A car accelerates down a hill (Fig. P4.87), going from rest to 30.0 m/s in 6.00 s. During the acceleration, a toy $(m=0.100 \mathrm{kg})$ hangs by a string from the car's ceiling. The acceleration is such that the string remains perpendicular to the ceiling. Determine (a) the angle $\theta$ and $(b)$ the tension in the string.

Zulfiqar A.
Numerade Educator

Problem 88

An inventive child wants to reach an apple in a tree without climbing the tree. Sitting in a chair connected to a rope that passes over a frictionless pulley (Fig. P4.88), the child pulls on the loose end of the rope with such a force that the spring scale reads 250 N. The child’s true weight is 320 N, and the chair weighs 160 N. The child’s feet are not touching the ground. (a) Show that the acceleration of the system is upward, and find its magnitude. (b) Find the force the child exerts on the chair.

Averell H.
Carnegie Mellon University

Problem 89

The parachute on a race car of weight 8820 $\mathrm{N}$ opens at the end of a quarter-mile run when the car is traveling at 35.0 $\mathrm{m} / \mathrm{s}$ . What total retarding force must be supplied by the parachute to stop the car in a distance of $1.00 \times 10^{3} \mathrm{m} ?$

Zulfiqar A.
Numerade Educator

Problem 90

A fire helicopter carries a $620-\mathrm{kg}$ bucket of water at the end of a 20.0 -m-long cable. Flying back from a fire at a constant speed of 40.0 $\mathrm{m} / \mathrm{s}$ , the cable makes an angle of $40.0^{\circ}$ with respect to the vertical. Determine the force exerted by air resistance on the bucket.

Averell H.
Carnegie Mellon University

Problem 91

The board sandwiched between two other boards in Figure $\mathrm{P} 4.91$ weighs 95.5 $\mathrm{N}$ . If the coefficient of friction between the boards is 0.663 , what must be the magnitude of the compression forces (assumed to be horizontal) acting on both sides of the center board to keep it from slipping?

Zulfiqar A.
Numerade Educator

Problem 92

A 72-kg man stands on a spring scale in an elevator. Starting from rest, the elevator ascends, attaining its maximum speed of 1.2 m/s in 0.80 s. The elevator travels with this constant speed for 5.0 s, undergoes a uniform negative acceleration for 1.5 s, and then comes to rest. What does the spring scale register (a) before the elevator starts to move? (b) During the first 0.80 s of the elevator’s ascent? (c) While the elevator is traveling at constant speed? (d) During the elevator’s negative acceleration?

Averell H.
Carnegie Mellon University