University Physics with Modern Physics

Wolfgang Bauer, Gary D. Westfall

Chapter 4

Force - all with Video Answers

Educators

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Chapter Questions

Problem 1

A car of mass $M$ travels in a straight line at constant speed along a level road with a coefficient of friction between the tires and the road of $\mu$ and a drag force of $D$. The magnitude of the net force on the car is
a) $\mu M g$.
c) $\sqrt{(\mu M g)^{2}+D^{2}}$
b) $\mu M g+D$.
d) zero.

Vishal Gupta

Vishal Gupta

Numerade Educator

Problem 1

A car of mass $M$ travels in a straight line at constant speed along a level road with a coefficient of friction between the tires and the road of $\mu$ and a drag force of $D$. The magnitude of the net force on the car is
a) $\mu M g$.
b) $\mu M g+D$.
c) $\sqrt{(\mu M g)^{2}+D^{2}}$
d) zero.

Vishal Gupta

Numerade Educator

Problem 2

A person stands on the surface of the Earth. The mass of the person is $m,$ and the mass of the Earth is $M .$ The person jumps upward, reaching a maximum height $h$ above the Earth. When the person is at this height $h,$ the magnitude of the force exerted on the Earth by the person is
a) $m g$
b) $M g$.
c) $M^{2} g / m$.
d) $m^{2} g / M$.
e) zero.

Sachin Rao

Numerade Educator

Problem 3

Leonardo da Vinci discovered that the magnitude of the friction force is simply proportional to the magnitude of the normal force only; that is, the friction force does not depend on the width or length of the contact area. Thus, the main reason to use wide tires on a race car is that they
a) look cool.
b) have more apparent contact area.
c) cost more.
d) can be made of softer materials.

Sachin Rao

Numerade Educator

Problem 4

The Tornado is a carnival ride that consists of a hollow vertical cylinder that rotates rapidly about its vertical axis. As the Tornado rotates, the riders are pressed against the inside wall of the cylinder by the rotation, and the floor of the cylinder drops away. The force that points upward, preventing the riders from falling downward, is
a) friction force.
b) a normal force.
c) gravity.
d) a tension force.

Sachin Rao

Numerade Educator

Problem 5

When a bus makes a sudden stop, passengers tend to jerk for ward. Which of Newton's laws can explain this?
a) Newton's First Law
b) Newton's Second Law
c) Newton's Third Law
d) It cannot be explained by Newton's laws.

Shahab Ullah

Numerade Educator

Problem 6

Only two forces, $\vec{F}_{1}$ and $\vec{F}_{2},$ are acting on a block. Which of the following can be the magnitude of the net force, $\vec{F}$, acting on the block (indicate all possibilities)?
a) $F>F_{1}+F_{2}$
b) $F=F_{1}+F_{2}$
c) $F<F_{1}+F_{2}$
d) none of the above

Shahab Ullah

Numerade Educator

Problem 7

Which of the following observations about the friction force is (are) incorrect?
a) The magnitude of the kinetic friction force is always proportional to the normal force.
b) The magnitude of the static friction force is always proportional to the normal force.
c) The magnitude of the static friction force is always proportional to the external applied force.
d) The direction of the kinetic friction force is always opposite the direction of the relative motion of the object with respect to the surface the object moves on.
e) The direction of the static friction force is always opposite that of the impending motion of the object relative to the surface it rests on.
f) All of the above are correct.

Sachin Rao

Numerade Educator

Problem 8

A horizontal force equal to the object's weight is applied to an object resting on a table. What is the acceleration of the moving object when the coefficient of kinetic friction between the object and floor is 1 (assuming the object is moving in the direction of the applied force)?
a) zero
b) $1 \mathrm{~m} / \mathrm{s}^{2}$
c) Not enough information is given to find the acceleration.

Sachin Rao

Numerade Educator

Problem 9

Two blocks of equal mass are connected by a massless horizontal rope and resting on a frictionless table. When one of the blocks is pulled away by a horizontal external force $\vec{F},$ what is the ratio of the net forces acting on the blocks?
a) 1: 1
b) 1: 1.41
c) 1: 2
d) none of the above

Sachin Rao

Numerade Educator

Problem 10

If a cart sits motionless on level ground, there are no forces acting on the cart.
a) true
b) false
c) maybe

Shahab Ullah

Numerade Educator

Problem 11

An object whose mass is $0.092 \mathrm{~kg}$ is initially at rest and then attains a speed of $75.0 \mathrm{~m} / \mathrm{s}$ in $0.028 \mathrm{~s}$. What average net force acted on the object during this time interval?
a) $1.2 \cdot 10^{2} \mathrm{~N}$
b) $2.5 \cdot 10^{2} \mathrm{~N}$
c) $2.8 \cdot 10^{2} \mathrm{~N}$
d) $4.9 \cdot 10^{2} \mathrm{~N}$

Sachin Rao

Numerade Educator

Problem 12

You push a large crate across the floor at constant speed, exerting a horizontal force $F$ on the crate. There is friction between the floor and the crate. The force of friction has a magnitude that is
a) zero.
b) $F$.
c) greater than $F$. information.
d) less than $F$.
e) impossible to quantify without further

Shahab Ullah

Numerade Educator

Problem 13

Which of the following fundamental forces are not apparent to us in our everyday lives?
a) gravitational force
b) electromagnetic force
c) strong nuclear force
d) weak nuclear force

Sachin Rao

Numerade Educator

Problem 14

An SUV of mass 3250 kg has a head-on collision with a $1250-\mathrm{kg}$ subcompact. Identify all the statements that are incorrect.
a) The SUV exerts a larger force on the subcompact than the subcompact exerts on the SUV.
b) The subcompact exerts a larger force on the SUV than the SUV exerts on the subcompact.
c) The subcompact experiences a larger acceleration than the SUV.
d) The SUV experiences a larger acceleration that the subcompact.

Sachin Rao

Numerade Educator

Problem 15

Which one of the following statements is correct?
a) The gravitational force on an object is always directed upward.
b) The gravitational force on an object is always directed downward.
c) The gravitational force on an object depends on the vertical speed of the object.
d) The gravitational force on an object depends on the horizontal speed of the object.

Sachin Rao

Numerade Educator

Problem 16

A normal force is a contact force that acts at the surface between two objects. Which of the following statements concerning the normal force is not correct?
a) The normal force is always equal to the force of gravity.
b) The normal force is just large enough to keep the two objects from penetrating each other.
c) The normal force is not necessarily equal to the force of gravity,
d) The normal force is perpendicular to the plane of the contact surface between the two objects.

Sachin Rao

Numerade Educator

Problem 17

You are at the shoe store to buy a pair of basketball shoes that have the greatest traction on a specific type of hardwood. To determine the coefficient of static friction, $\mu,$ you place each shoe on a plank of the wood and tilt the plank to an angle $\theta$, at which the shoe just starts to slide. Obtain an expression for $\mu$ as a function of $\theta$

Sachin Rao

Numerade Educator

Problem 18

A heavy wooden ball is hanging from a ceiling by a piece of string that is attached to the ceiling and to the top of the ball. A similar piece of string

Sachin Rao

Numerade Educator

Problem 19

A car pulls a trailer down the highway. Let $F_{\mathrm{t}}$ be the magnitude of the force on the trailer due to the car, and let $F_{c}$ be the magnitude of the force on the car due to the trailer. If the car and trailer are moving at a constant velocity across level ground, then $F_{t}=F_{c}$. If the car and trailer are accelerating up a hill, what is the relationship between the two forces?

Sachin Rao

Numerade Educator

Problem 20

A car accelerates down a level highway. What is the force in the direction of motion that accelerates the car?

Sachin Rao

Numerade Educator

Problem 21

If the forces that two interacting objects exert on each other are always exactly equal in magnitude and opposite in direction, how is it possible for an object to accelerate?

Sachin Rao

Numerade Educator

Problem 22

True or false: A physics book on a table will not move at all if and only if the net force is zero.

Shahab Ullah

Numerade Educator

Problem 23

A mass slides on a ramp that is at an angle of $\theta$ above the horizontal. The coefficient of friction between the mass and the ramp is $\mu$.
a) Find an expression for the magnitude and direction of the acceleration of the mass as it slides up the ramp.
b) Repeat part (a) to find an expression for the magnitude and direction of the acceleration of the mass as it slides down the ramp.

Sachin Rao

Numerade Educator

Problem 25

A block is sliding on a (near) frictionless slope with an incline of $30.0^{\circ} .$ Which force is greater in magnitude, the net force acting on the block or the normal force acting on the block?

Sachin Rao

Numerade Educator

Problem 26

A tow truck of mass $M$ is using a cable to pull a shipping container of mass $m$ across a horizontal surface as shown in the figure. The cable is attached to the container at the front bottom corner and makes an angle $\theta$ with the vertical as shown. The coefficient of kinetic friction between the surface and the crate is $\mu$
a) Draw a free-body diagram for the container.
b) Assuming that the truck pulls the container at a constant speed, write an equation for the magnitude $T$ of the string tension in the cable.

Sachin Rao

Numerade Educator

Problem 27

4.27 The gravitational acceleration on the Moon is a sixth of that on Earth. The weight of an apple is $1.00 \mathrm{~N}$ on Earth.
a) What is the weight of the apple on the Moon?
b) What is the mass of the apple?

Shahab Ullah

Numerade Educator

Problem 28

A $423.5-\mathrm{N}$ force accelerates a go-cart and its driver from $10.4 \mathrm{~m} / \mathrm{s}$ to $17.9 \mathrm{~m} / \mathrm{s}$ in $5.00 \mathrm{~s}$. What is the mass of the go-cart plus driver?

Shahab Ullah

Numerade Educator

Problem 29

You have just joined an exclusive health club, located on the top floor of a skyscraper. You reach the facility by using an express elevator. The elevator has a precision scale installed so that members can weigh themselves before and after their workouts. A member steps into the elevator and gets on the scale before the elevator doors close. The scale shows a weight of 183.7 lb. Then the elevator accelerates upward with an acceleration of $2.43 \mathrm{~m} / \mathrm{s}^{2},$ while the member is still standing on the scale. What is the weight shown by the scale's display while the elevator is accelerating?

Sachin Rao

Numerade Educator

Problem 30

An elevator cabin has a mass of $358.1 \mathrm{~kg}$, and the combined mass of the people inside the cabin is $169.2 \mathrm{~kg}$. The cabin is pulled upward by a cable, with a constant acceleration of $4.11 \mathrm{~m} / \mathrm{s}^{2} .$ What is the tension in the cable?

Sachin Rao

Numerade Educator

Problem 31

An elevator cabin has a mass of $363.7 \mathrm{~kg},$ and the combined mass of the people inside the cabin is $177.0 \mathrm{~kg} .$ The cabin is pulled upward by a cable, in which there is a tension force of $7638 \mathrm{~N}$. What is the acceleration of the elevator?

Sachin Rao

Numerade Educator

Problem 32

Two blocks are in contact on a frictionless, horizontal tabletop. An external force, $\vec{F},$ is applied to block $1,$ and the two blocks are moving with a constant acceleration of $2.45 \mathrm{~m} / \mathrm{s}^{2} .$ Use $M_{1}=3.20 \mathrm{~kg}$ and $M_{2}=5.70 \mathrm{~kg}$
a) What is the magnitude, $F$, of the applied force?
b) What is the contact force between the blocks?
c) What is the net force acting on block $1 ?$

Sachin Rao

Numerade Educator

Problem 33

-4.33 The density (mass per unit volume) of ice is $917 \mathrm{~kg} / \mathrm{m}^{3},$ and the density of seawater is $1024 \mathrm{~kg} / \mathrm{m}^{3}$. Only $10.45 \%$ of the volume of an iceberg is above the water's surface. If the volume of a particular iceberg that is above water is $4205.3 \mathrm{~m}^{3}$, what is the magnitude of the force that the seawater exerts on this iceberg?

Sachin Rao

Numerade Educator

Problem 34

In a physics laboratory class, three massless ropes are tied together at a point. A pulling force is applied along each rope: $F_{1}=150 . \mathrm{N}$ at $60.0^{\circ}$ $F_{2}=200 . \mathrm{N}$ at $100 .^{\circ}, F_{3}=100 . \mathrm{N}$ at $190 .^{\circ} .$ What is the magnitude of a fourth force and the angle at which it acts to keep the point at the center of the system stationary? (All angles are measured from the positive $x$ -axis.)

Sachin Rao

Numerade Educator

Problem 35

Four weights, of masses $m_{1}=6.50 \mathrm{~kg}, m_{2}=3.80 \mathrm{~kg}$, $m_{3}=10.70 \mathrm{~kg}$, and $m_{4}=4.20 \mathrm{~kg}$, are hanging from a ceiling as shown in the figure. They are connected with ropes. What is the tension in the rope connecting masses $m_{1}$ and $m_{2} ?$

Sachin Rao

Numerade Educator

Problem 36

A hanging mass, $M_{1}=0.500 \mathrm{~kg}$, is attached by a light string that runs over a frictionless pulley to a mass $M_{2}=1.50 \mathrm{~kg}$ that is initially at rest on a frictionless table. Find the magnitude of the acceleration, $a$, of $M_{2}$.

Sachin Rao

Numerade Educator

Problem 37

A hanging mass, $M_{1}=0.500 \mathrm{~kg}$, is attached by a light string that runs over a frictionless pulley to the front of a mass $M_{2}=1.50 \mathrm{~kg}$ that is initially at rest on a frictionless table. A third mass $M_{3}=2.50 \mathrm{~kg}$, which is also initially at rest on the same frictionless table, is attached to the back of $M_{2}$ by a light string.
a) Find the magnitude of the acceleration, $a,$ of mass $M_{3}$.
b) Find the tension in the string between masses $M_{1}$ and $M_{2}$.

Sachin Rao

Numerade Educator

Problem 38

A hanging mass, $M_{1}=0.400 \mathrm{~kg}$, is attached by a light string that runs over a frictionless pulley to a mass $M_{2}=1.20 \mathrm{~kg}$ that is initially at rest on a frictionless ramp. The ramp is at an angle of $\theta=30.0^{\circ}$ above the horizontal, and the pulley is at the top of the ramp. Find the magnitude and direction of the acceleration, $a_{2},$ of $M_{2}$

Sachin Rao

Numerade Educator

Problem 39

A force table is a circular table with a small ring that is to be balanced in the center of the table. The ring is attached to three hanging masses by strings of negligible mass that pass over frictionless pulleys mounted on the edge of the table. The magnitude and direction of each of the three horizontal forces acting on the ring can be adjusted by changing the amount of each hanging mass and the position of each pulley, respectively. Given a mass $m_{1}=0.0400$ kg pulling in the positive $x$ -direction and a mass $m_{2}=0.0300$ kg pulling in the positive $y$ -direction, find the mass $\left(m_{3}\right)$ and the angle $(\theta,$ counterclockwise from the positive $x$ -axis) that will balance the ring in the center of the table.

Sachin Rao

Numerade Educator

Problem 40

A monkey is sitting on a wood plate attached to a rope whose other end is passed over a tree branch, as shown in the figure. The monkey holds the rope and tries to pull it down. The combined mass of the monkey and the wooc plate is $100 . \mathrm{kg} .$ Assume that you can neglect the friction between the rope and the branch.
a) What is the minimum force the monkey has to apply to lift itself and the plate off the ground?
b) What applied force is needed to move the monkey with an upward acceleration of $2.45 \mathrm{~m} / \mathrm{s}^{2} ?$

Sachin Rao

Numerade Educator

Problem 41

4.41 A bosun's chair is a device used by a boatswain to lift himself to the top of the mainsail of a ship. A simplified device consists of a chair, a rope of negligible mass, and a frictionless pulley attached to the top of the mainsail. The rope goes over the pulley, with one end attached to the chair, and the boatswain pulls on the other end, lifting himself upward. The chair and boatswain have a total mass $M=90.0 \mathrm{~kg}$.
a) If the boatswain is pulling himself up at a constant speed, with what magnitude of force must he pull on the rope?
b) If, instead, the boatswain moves in a jerky fashion, accelerating upward with a maximum acceleration of magnitude $a=2.00 \mathrm{~m} / \mathrm{s}^{2},$ with what maximum magnitude of force must he pull on the rope?

Sachin Rao

Numerade Educator

Problem 42

4.42 A granite block of mass $3311 \mathrm{~kg}$ is suspended from a pulley system as shown in the figure. The rope is wound around the pulleys 6 times. What is the force with which you would have to pull on the rope to hold the granite block in equilibrium?

Narayan Hari

Numerade Educator

Problem 43

Arriving on a newly discovered planet, the captain of a spaceship performed the following experiment to calculate the gravitational acceleration for the planet: She placed masses of $100.0 \mathrm{~g}$ and $200.0 \mathrm{~g}$ on an Atwood device made of massless string and a frictionless pulley and measured that it took $1.52 \mathrm{~s}$ for each mass to travel $1.00 \mathrm{~m}$ from rest.
a) What is the gravitational acceleration for the planet?
b) What is the tension in the string?

Sachin Rao

Numerade Educator

Problem 44

A store sign of mass $4.25 \mathrm{~kg}$ is hung by two wires that each make an angle of $\theta=42.4^{\circ}$ with the ceiling. What is the tension in each wire?

Sachin Rao

Numerade Educator

Problem 45

A crate of oranges slides down an inclined plane without friction. If it is released from rest and reaches
a speed of $5.832 \mathrm{~m} / \mathrm{s}$ after sliding a distance of $2.29 \mathrm{~m}$, what is the angle of inclination of the plane with respect to the horizontal?

Sachin Rao

Numerade Educator

Problem 46

A load of bricks of mass $M=200.0 \mathrm{~kg}$ is attached to a crane by a cable of negligible mass and length $L=3.00 \mathrm{~m}$. Initially, when the cable hangs vertically downward, the bricks are a horizontal distance $D=1.50 \mathrm{~m}$ from the wall where the bricks are to be placed. What is the magnitude of the horizontal force that must be applied to the load of bricks (without moving the crane) so that the bricks will rest directly above the wall?

Sachin Rao

Numerade Educator

Problem 47

A large ice block of mass $M=80.0 \mathrm{~kg}$ is held stationary on a frictionless ramp. The ramp is at an angle of $\theta=36.9^{\circ}$ above the horizontal.
a) If the ice block is held in place by a tangential force along the surface of the ramp (at angle $\theta$ above the horizontal), find the magnitude of this force.
b) If, instead, the ice block is held in place by a horizontal force, directed horizontally toward the center of the ice block, find the magnitude of this force.

Sachin Rao

Numerade Educator

Problem 48

A mass, $m_{1}=20.0 \mathrm{~kg},$ on a frictionless ramp is attached to a light string. The string passes over a frictionless pulley and is attached to a hanging mass, $m_{2}$ The ramp is at an angle of $\theta=30.0^{\circ}$ above the horizontal. The mass $m_{1}$, moves up the ramp uniformly (at constant speed). Find the value of
$m_{2}$

Sachin Rao

Numerade Educator

Problem 49

A piñata of mass $M=8.00 \mathrm{~kg}$ is attached to a rope of negligible mass that is strung between the tops of two vertical poles. The horizontal distance between the poles is $D=2.00 \mathrm{~m},$ and the top of the right pole is a vertical distance $h=0.500 \mathrm{~m}$ higher than the top of the left pole. The piñata is attached to the rope at a horizontal position halfway between the two poles and at a vertical distance $s=1.00 \mathrm{~m}$ below the top of the left pole. Find the tension in each part of the rope due to the weight of the piñata.

Sachin Rao

Numerade Educator

Problem 50

A piñata of mass $M=12.0 \mathrm{~kg}$ hangs on a rope of negligible mass that is strung between the tops of two vertical poles. The horizontal distance between the poles is $D=2.00 \mathrm{~m},$ the top of the right pole is a vertical distance $h=0.500 \mathrm{~m}$ higher than the top of the left pole, and the total length of the rope between the poles is $L=3.00 \mathrm{~m} .$ The piñata is attached to a ring, with the rope passing through the center of the ring. The ring is frictionless, so that it can slide freely along the rope until the piñata comes to a point of static equilibrium.
a) Determine the distance from the top of the left (lower) pole to the ring when the pinata is in static equilibrium.
b) What is the tension in the rope when the pinata is at this point of static equilibrium?

Eduard Sanchez

Numerade Educator

Problem 51

Three objects with masses $m_{1}=36.5 \mathrm{~kg}$ $m_{2}=19.2 \mathrm{~kg}$, and $m_{3}=12.5 \mathrm{~kg}$ are hanging from ropes that run over pulleys. What is the acceleration of $m_{1} ?$

Sachin Rao

Numerade Educator

Problem 52

- 4.52 A rectangular block of width $w=116.5 \mathrm{~cm}$ depth $d=164.8 \mathrm{~cm},$ and height $h=105.1 \mathrm{~cm}$ is cut diagonally from one upper corner to the opposing lower corners so that a triangular surface is generated, as shown in the figure. A paperweight of mass $m=16.93 \mathrm{~kg}$ is sliding down the incline without friction. What is the magnitude of the acceleration that the paperweight experiences?

Sachin Rao

Numerade Educator

Problem 53

A large cubical block of ice of mass $M=64.0 \mathrm{~kg}$ and sides of length $L=0.400 \mathrm{~m}$ is held stationary on a frictionless ramp. The ramp is at an angle of $\theta=26.0^{\circ}$ above the horizontal. The ice cube is held in place by a rope of negligible mass and length $l=1.60 \mathrm{~m}$. The rope is attached to the surface of the ramp and to the upper edge of the ice cube, a distance $L$ above the surface of the ramp. Find the tension in the rope.

Sachin Rao

Numerade Educator

Problem 54

A bowling ball of mass $M_{1}=6.00 \mathrm{~kg}$ is initially at rest on the sloped side of a wedge of mass $M_{2}=9.00 \mathrm{~kg}$ that is on a frictionless horizontal floor. The side of the wedge is sloped at an angle of $\theta=36.9^{\circ}$ above the horizontal.
a) What is the magnitude of the horizontal force that should be exerted on the bowling ball to keep it at a constant height on the slope?
b) What is the magnitude of the acceleration of the wedge, if no external force is applied?

Vishal Gupta

Numerade Educator

Problem 55

A skydiver of mass $82.3 \mathrm{~kg}$ (including outfit and equipment) floats downward suspended from her parachute, having reached terminal speed. The drag coefficient is 0.533 , and the area of her parachute is $20.11 \mathrm{~m}^{2}$. The density of air is $1.14 \mathrm{~kg} / \mathrm{m}^{3}$. What is the air's drag force on her?

Sachin Rao

Numerade Educator

Problem 56

The elapsed time for a top fuel dragster to start from rest and travel in a straight line a distance of $\frac{1}{4}$ mile $(402 \mathrm{~m})$ is $4.441 \mathrm{~s}$. Find the minimum coefficient of friction between the tires and the track needed to achieve this result. (Note that the minimum coefficient of friction is found from the simplifying assumption that the dragster accelerates with constant acceleration. For this problem we neglect the downward forces from spoilers and the exhaust pipes.)

Vishal Gupta

Numerade Educator

Problem 57

An engine block of mass $M$ is on the flatbed of a pickup truck that is traveling in a straight line down a level road with an initial speed of $30.0 \mathrm{~m} / \mathrm{s}$. The coefficient of static friction between the block and the bed is $\mu_{s}=0.540 .$ Find the minimum distance in which the truck can come to a stop without the engine block sliding toward the cab.

Sachin Rao

Numerade Educator

Problem 58

A box of books is initially at rest a distance $D=0.540 \mathrm{~m}$ from the end of a wooden board. The coefficient of static friction between the box and the board is $\mu_{\mathrm{s}}=0.320$, and the coefficient of kinetic friction is $\mu_{\mathrm{k}}=0.250 .$ The angle of the board is increased slowly, until the box just begins to slide; then the board is held at this angle. Find the speed of the box as it reaches the end of the board.

Sachin Rao

Numerade Educator

Problem 59

A block of mass $M_{1}=0.640 \mathrm{~kg}$ is initially at rest on a cart of mass $M_{2}=0.320 \mathrm{~kg}$ with the cart initially at rest on a level air track. The coefficient of static friction between the block and the cart is $\mu_{\mathrm{s}}=0.620$, but there is essentially no friction between the air track and the cart. The cart is accelerated by a force of magnitude $F$ parallel to the air track. Find the maximum value of $F$ that allows the block to accelerate with the cart, without sliding on top of the cart.

Sachin Rao

Numerade Educator

Problem 60

Coffee filters behave like small parachutes, with a drag force that is proportional to the velocity squared, $F_{\text {drag }}=K v^{2} .$ A single coffee filter, when dropped from a height of $2.00 \mathrm{~m},$ reaches the ground in a time of $3.00 \mathrm{~s}$. When a second coffee filter is nestled within the first, the drag coefficient remains the same, but the weight is doubled. Find the time for the combined filters to reach the ground. (Neglect the brief period when the filters are accelerating up to their terminal speed.)

Bettina Hanlon

Numerade Educator

Problem 61

Your refrigerator has a mass of $112.2 \mathrm{~kg}$, including the food in it. It is standing in the middle of your kitchen, and you need to move it. The coefficients of static and kinetic friction between the fridge and the tile floor are 0.460 and 0.370 , respectively. What is the magnitude of the force of friction acting on the fridge, if you push against it horizontally with a force of each magnitude?
a) $300.0 \mathrm{~N}$
b) $500.0 \mathrm{~N}$
c) $700.0 \mathrm{~N}$

Sachin Rao

Numerade Educator

Problem 62

On the bunny hill at a ski resort, a towrope pulls the skiers up the hill with constant speed of $1.74 \mathrm{~m} / \mathrm{s}$. The slope of the hill is $12.4^{\circ}$ with respect to the horizontal. A child is being pulled up the hill. The coefficients of static and kinetic friction between the child's skis and the snow are 0.152 and 0.104 respectively, and the child's mass is $62.4 \mathrm{~kg}$, including clothing and equipment. What is the force with which the towrope has to pull on the child?

Sachin Rao

Numerade Educator

Problem 63

A skier starts with a speed of $2.00 \mathrm{~m} / \mathrm{s}$ and skis straight down a slope with an angle of $15.0^{\circ}$ relative to the horizontal. The coefficient of kinetic friction between her skis and the snow is $0.100 .$ What is her speed after 10.0 s?

Sachin Rao

Numerade Educator

Problem 64

A block of mass $m_{1}=21.9 \mathrm{~kg}$ is at rest on a plane inclined at $\theta=30.0^{\circ}$ above the horizontal. The block is connected via a rope and massless pulley system to another block of mass $m_{2}=25.1 \mathrm{~kg}$, as shown in the figure. The coefficients of static and kinetic friction between block 1 and the inclined plane are $\mu_{s}=0.109$ and $\mu_{\mathrm{k}}=0.086,$ respectively. If the blocks are released from rest. what is the displacement of block 2 in the vertical direction after 1.51 s? Use positive numbers for the upward direction and negative numbers for the
downward direction.

Vishal Gupta

Numerade Educator

Problem 65

A wedge of mass $m=36.1 \mathrm{~kg}$ is located on a plane that is inclined by an angle $\theta=21.3^{\circ}$ with respect to the horizontal. A force $F=302.3 \mathrm{~N}$ in the horizontal direction pushes on the wedge, as shown in the figure. The coefficient of kinetic friction between the wedge and the plane is $0.159 .$ What is the acceleration of the wedge along the plane?

Sachin Rao

Numerade Educator

Problem 66

A chair of mass $M$ rests on a level floor, with a coefficient of static friction $\mu_{\mathrm{s}}=0.560$ between the chair and the floor. A person wishes to push the chair across the floor. He pushes downward on the chair with a force $F$ at an angle $\theta$ relative to the horizontal. What is the minimum value of $\theta$ for which the chair will not start to move across the floor, no matter how large $F$ gets?

Bettina Hanlon

Numerade Educator

Problem 67

As shown in the figure, blocks of masses $m_{1}=250.0 \mathrm{~g}$ and $m_{2}=500.0 \mathrm{~g}$ are attached by a massless string over a frictionless and massless pulley. The coefficients of static and kinetic friction between the block and inclined plane are 0.250 and 0.123 , respectively. The angle of the incline is $\theta=30.0^{\circ}$ and the blocks are at rest initially.
a) In which direction do the blocks
move?
b) What is the acceleration of the blocks?

Prashant Bana

Numerade Educator

Problem 68

A block of mass $M=500.0 \mathrm{~g}$ sits on a horizontal tabletop. The coefficients of static and kinetic friction are 0.530 and 0.410 , respectively, at the contact surface between table and block. The block is pushed on with a $10.0 \mathrm{~N}$ external force at an angle $\theta$ with the horizontal.
a) What angle will lead to the maximum acceleration of the block for a given pushing force?
b) What is the maximum acceleration?

Eduard Sanchez

Numerade Educator

Problem 69

A car without ABS (antilock brake system) was moving at $15.0 \mathrm{~m} / \mathrm{s}$ when the driver slammed on the brakes to make a sudden stop. The coefficients of static and kinetic friction between the tires and the road are 0.550 and $0.430,$ respectively.
a) What was the acceleration of the car during the interval between braking and stopping?
b) How far did the car travel before it stopped?

Sachin Rao

Numerade Educator

Problem 70

A $2.00-\mathrm{kg}$ block $\left(M_{1}\right)$ and a $6.00-\mathrm{kg}$ block $\left(M_{2}\right)$ are connected by a massless string. Applied forces, $F_{1}=10.0 \mathrm{~N}$ and $F_{2}=5.00 \mathrm{~N},$ act on the blocks, as shown in the figure.
a) What is the acceleration of the blocks?
b) What is the tension in the string?
c) What is the net force acting on $M_{1}$ ? (Neglect friction between the blocks and the table.)

Susan Hallstrom

Susan Hallstrom

Numerade Educator

Problem 71

An elevator contains two masses: $M_{1}=2.00 \mathrm{~kg}$ is attached by a string (string 1 ) to the ceiling of the elevator, and $M_{2}=4.00 \mathrm{~kg}$ is attached by a similar string (string 2) to the bottom of mass $1 .$
a) Find the tension in string $1\left(T_{1}\right)$ if the elevator is moving upward at a constant velocity of $v=3.00 \mathrm{~m} / \mathrm{s}$
b) Find $T_{1}$ if the elevator is accelerating upward with an acceleration of $a=3.00 \mathrm{~m} / \mathrm{s}^{2}$

Sachin Rao

Numerade Educator

Problem 71

An elevator contains two masses: $M_{1}=2.00 \mathrm{~kg}$ is attached by a string (string 1 ) to the ceiling of the elevator, and $M_{2}=4.00 \mathrm{~kg}$ is attached by a similar string (string 2) to the bottom of mass 1 .
a) Find the tension in string $1\left(T_{1}\right)$ if the elevator is moving upward at a constant velocity of $v=3.00 \mathrm{~m} / \mathrm{s}$
b) Find $T_{1}$ if the elevator is accelerating upward with an acceleration of $a=3.00 \mathrm{~m} / \mathrm{s}^{2}$

Sachin Rao

Numerade Educator

Problem 72

What coefficient of friction is required to stop a hockey puck sliding at $12.5 \mathrm{~m} / \mathrm{s}$ initially over a distance of $60.5 \mathrm{~m} ?$

Sachin Rao

Numerade Educator

Problem 73

A spring of negligible mass is attached to the ceiling of an elevator. When the elevator is stopped at the first floor, a mass $M$ is attached to the spring, stretching the spring a distance $D$ until the mass is in equilibrium. As the elevator starts upward toward the second floor, the spring stretches an additional distance $D / 4$. What is the magnitude of the acceleration of the elevator? Assume the force provided by the spring is linearly proportional to the distance stretched by the spring.

Eduard Sanchez

Numerade Educator

Problem 74

A crane of mass $M=1.00 \cdot 10^{4} \mathrm{~kg}$ lifts a wrecking ball of mass $m=1200 . \mathrm{kg}$ directly upward.
a) Find the magnitude of the normal force exerted on the crane by the ground while the wrecking ball is moving upward at a constant speed of $v=1.00 \mathrm{~m} / \mathrm{s}$
b) Find the magnitude of the normal force if the wrecking ball's upward motion slows at a constant rate from its initial speed $v=1.00 \mathrm{~m} / \mathrm{s}$ to a stop over a distance $D=0.250 \mathrm{~m}$.

Eduard Sanchez

Numerade Educator

Problem 75

A block of mass 20.0 kg supported by a vertical massless cable is initially at rest. The block is then pulled upward with a constant acceleration of $2.32 \mathrm{~m} / \mathrm{s}^{2}$
a) What is the tension in the cable?
b) What is the net force acting on the mass?
c) What is the speed of the block after it has traveled $2.00 \mathrm{~m} ?$

Sachin Rao

Numerade Educator

Problem 75

A block of mass $20.0 \mathrm{~kg}$ supported by a vertical massless cable is initially at rest. The block is then pulled upward with a constant acceleration of $2.32 \mathrm{~m} / \mathrm{s}^{2}$
a) What is the tension in the cable?
b) What is the net force acting on the mass?
c) What is the speed of the block after it has traveled $2.00 \mathrm{~m}$ ?

Sachin Rao

Numerade Educator

Problem 76

Three identical blocks, $\mathrm{A}, \mathrm{B},$ and $\mathrm{C},$ are on a horizontal frictionless between the other two blocks. If block $\mathrm{C}$ is pulled horizontally by a force of magnitude $F=12.0 \mathrm{~N},$ find the tension in the string between blocks $\mathrm{B}$ and $C$.

Sachin Rao

Numerade Educator

Problem 76

Three identical blocks, $A, B$, and $C$, are on a horizontal frictionless table. The blocks are connected by strings of negligible mass, with block B between the other two blocks. If block $\mathrm{C}$ is pulled horizontally by a force of magnitude $F=12.0 \mathrm{~N}$, find the tension in the string between blocks $\mathrm{B}$ and $C$.

Sachin Rao

Numerade Educator

Problem 77

A block of mass $m_{1}=3.00 \mathrm{~kg}$ and a block of mass $m_{2}=4.00 \mathrm{~kg}$ are suspended by a massless string over a frictionless pulley with negligible mass, as in an Atwood machine. The blocks are held motionless and then released. What is the acceleration of the two blocks?

Sachin Rao

Numerade Educator

Problem 78

.4 .78 Two blocks of masses $m_{1}$ and $m_{2}$ are suspended by a massless string over a frictionless pulley with negligible mass, as in an Atwood machine. The blocks are held motionless and then released. If $m_{1}=3.50 \mathrm{~kg},$ what value does $m_{2}$ have to have for the system to experience an acceleration of $a=0.400 \mathrm{~g}$ ? (Hint: There are two solutions to this problem.)

Sachin Rao

Numerade Educator

Problem 79

A tractor pulls a sled of mass $M=1000$. kg across level ground. The coefficient of kinetic friction between the sled and the ground is $\mu_{\mathrm{k}}=0.600 .$ The tractor pulls the sled by a rope that connects to the sled at an angle of $\theta=30.0^{\circ}$ above the horizontal. What magnitude of tension in the rope is necessary to move the sled horizontally with an acceleration $a=2.00 \mathrm{~m} / \mathrm{s}^{2}$ ?

Sachin Rao

Numerade Educator

Problem 80

A $2.00-\mathrm{kg}$ block is on a plane inclined at $20.0^{\circ}$ with respect to the horizontal. The coefficient of static friction between the block and the plane is $0.600 .$
a) How many forces are acting on the block?
b) What is the normal force?
c) Is this block moving? Explain.

Sachin Rao

Numerade Educator

Problem 81

A block of mass $5.00 \mathrm{~kg}$ is sliding at a constant velocity down an inclined plane that makes an angle of $37.0^{\circ}$ with respect to the horizontal.
a) What is the friction force?
b) What is the coefficient of kinetic friction?

Nishant Kumar

Numerade Educator

Problem 82

A skydiver of mass $83.7 \mathrm{~kg}$ (including outfit and equipment) falls in the spread-eagle position, having reached terminal speed. Her drag coefficient is $0.587,$ and her surface area that is exposed to the air stream is $1.035 \mathrm{~m}^{2} .$ How long does it take her to fall a vertical distance of $296.7 \mathrm{~m} ?$ (The density of air is $\left.1.14 \mathrm{~kg} / \mathrm{m}^{3} .\right)$

Bettina Hanlon

Numerade Educator

Problem 83

A 0.500 -kg physics textbook is hanging from two massless wires of equal length attached to a ceiling. The tension on each wire is measured as $15.4 \mathrm{~N}$. What is the angle of the wires with the horizontal?

Sachin Rao

Numerade Educator

Problem 84

In the figure, an external force $\vec{F}$ is holding a bob of mass $500 . \mathrm{g}$ in a station ary position. The angle that the massless rope makes with the vertical is $\theta=30.0^{\circ}$
a) What is the magnitude, $F$, of the force needed to maintain equilibrium?
b) What is the tension in the rope?

Sachin Rao

Numerade Educator

Problem 85

In a physics class, a 2.70 -g ping-pong ball was suspended from a massless string. The string makes an angle of $\theta=15.0^{\circ}$ with the vertical when air is blown horizontally at the ball at a speed of $20.5 \mathrm{~m} / \mathrm{s}$. Assume that the friction force is proportional to the squared speed of the air stream.
a) What is the proportionality constant in this experiment?
b) What is the tension in the string?

Bettina Hanlon

Numerade Educator

Problem 86

A nano wire is a (nearly) one-dimensional structure with a diameter on the order of a few nanometers. Suppose a 100.0 -nm-long nanowire made of pure silicon (density of $\mathrm{Si}=2.33 \mathrm{~g} / \mathrm{cm}^{3}$ ) has a diameter of $5.00 \mathrm{nm}$. This nanowire is attached at the top and hanging down vertically due to the force of gravity.

Eduard Sanchez

Numerade Educator

Problem 87

Two blocks are stacked on a frictionless table, and a horizontal force $F$ is applied to the top block (block 1). Their masses are $m_{1}=2.50 \mathrm{~kg}$ and $m_{2}=3.75 \mathrm{~kg} .$ The coefficients of static and kinetic friction between the blocks are 0.456 and 0.380 , respectively.
a) What is the maximum applied force $F$ for which $m_{1}$ will not slide off $m_{2}$ ?
b) What are the accelerations of $m_{1}$ and $m_{2}$ when the force $F=24.5 \mathrm{~N}$ is applied to $m_{1} ?$

Eduard Sanchez

Numerade Educator

Problem 88

Two blocks $\left(m_{1}=1.23 \mathrm{~kg}\right.$ and $m_{2}=2.46 \mathrm{~kg}$ ) are glued together and are moving downward on an inclined plane having an angle of $40.0^{\circ}$ with respect to the horizontal. Both blocks are lying flat on the surface of the inclined plane. The coefficients of kinetic friction are 0.23 for $m_{1}$ and 0.35 for $m_{2}$. What is the acceleration of the blocks?

Sachin Rao

Numerade Educator

Problem 89

A marble block of mass $m_{1}=567.1 \mathrm{~kg}$ and a granite block of mass

Paul A.

California State Polytechnic University, Pomona

Problem 89

A marble block of mass $m_{1}=559.1 \mathrm{~kg}$ and a granite block of mass $m_{2}=128.4 \mathrm{~kg}$ are connected to each other by a rope that runs over a pulley as shown in the figure with Problem $4.89 .$ Both blocks are located on inclined planes with angles $\alpha=38.3^{\circ}$ and $\beta=57.2^{\circ} .$ The rope glides over the pulley without friction, but the coefficient of friction between block 1 and the inclined plane is $\mu_{1}=0.130,$ and that between block 2 and the inclined plane is $\mu_{2}=0.310 .$ (For simplicity, assume that the coefficients of static and kinetic friction are the same in each case.) What i the acceleration of the marble block? Note that the positive $x$ -direction is indicated in the figure.

Vishal Gupta

Numerade Educator

Problem 90

A marble block of mass $m_{1}=559.1 \mathrm{~kg}$ and a granite block of mass $m_{2}=128.4 \mathrm{~kg}$ are connected to each other by a rope that runs over a pulley as shown in the figure with Problem $4.89 .$ Both blocks are located on inclined planes with angles $\alpha=38.3^{\circ}$ and $\beta=57.2^{\circ} .$ The rope glides over the pulley without friction, but the coefficient of friction between block 1 and the inclined plane is $\mu_{1}=0.130$, and that between block 2 and the inclined plane is $\mu_{2}=0.310 .$ (For simplicity, assume that the coefficients of static and kinetic friction are the same in each case.) What is the acceleration of the marble block? Note that the positive $x$ -direction is indicated in the figure.

LB

Laura Bravo

Numerade Educator

Problem 91

As shown in the figure, two masses, $m_{1}=3.50 \mathrm{~kg}$ and $m_{2}=5.00 \mathrm{~kg}$. are on a frictionless tabletop and mass $m_{3}=7.60 \mathrm{~kg}$ is hanging from $m_{1}$. The coefficients of static and kinetic friction between $m_{1}$ and $m_{2}$ are 0.600 and $0.500,$ respectively.
a) What are the accelerations of $m_{1}$ and $m_{2}$ ?
b) What is the tension in the string between $m_{1}$ and $m_{3}$ ?

Sachin Rao

Numerade Educator

Problem 92

A block of mass $m_{1}=2.30 \mathrm{~kg}$ is placed in front of a block of mass $m_{2}=5.20 \mathrm{~kg},$ as shown in the figure. The coefficient of static friction between $m_{1}$ and $m_{2}$ is $0.65,$ and there is negligible friction between the larger block and the tabletop.
a) What forces are acting on $m_{1} ?$
b) What is the minimum external force $F$ that can be applied to $m_{2}$ so that $m_{1}$ does not fall?
c) What is the contact force between $m_{1}$ and $m_{2} ?$
d) What is the net force acting on $m_{2}$ when the force found in part (b) is applied?

Eduard Sanchez

Numerade Educator

Problem 93

A suitcase of weight $M g=450 .$ N is being pulled by a small strap across a level floor. The coefficient of kinetic friction between the suitcase
and the floor is $\mu_{\mathrm{k}}=0.640 .$
a) Find the optimal angle of the strap above the horizontal. (The optimal angle minimizes the force necessary to pull the suitcase at constant speed.)
b) Find the minimum tension in the strap needed to pull the suitcase at constant speed.

Penny Riley

Numerade Educator

Problem 94

As shown in the figure, a block of mass $M_{1}=0.450 \mathrm{~kg}$ is initially at rest on a slab of mass $M_{2}=0.820 \mathrm{~kg}$, and the slab is initially at rest on a level table. A string of negligible mass is connected to the slab, runs over a frictionless pulley on the edge of the table, and is attached to a hanging mass $M_{3}$. The block rests on the slab but is not tied to the string, so friction provides the only horizontal force on the block. The slab has a coefficient of kinetic friction $\mu_{\mathrm{k}}=0.340$ and a coefficient of static friction $\mu_{\mathrm{s}}=0.560$ with both the table and the block. When released, $M_{3}$ pulls on the string and accelerates the slab, which accelerates the block. Find the maximum mass of $M_{3}$ that allows the block to accelerate with the slab, without sliding on top of the slab.

LB

Laura Bravo

Numerade Educator

Problem 95

- 4.95 As shown in the figure with Problem 4.94 , a block of mass $M_{1}=0.250 \mathrm{~kg}$ is initially at rest on a slab of mass $M_{2}=0.420 \mathrm{~kg}$, and the slab is initially at rest on a level table. A string of negligible mass is connected to the slab, runs over a frictionless pulley on the edge of the table, and is attached to a hanging mass $M_{3}=1.80 \mathrm{~kg} .$ The block rests on the slab but is not tied to the string, so friction provides the only horizontal force on the block. The slab has a coefficient of kinetic friction $\mu_{\mathrm{k}}=0.340$ with both the table and the block. When released, $M_{3}$ pulls on the string, which accelerates the slab so quickly that the block starts to slide on the slab. Before the block slides off the top of the slab:
a) Find the magnitude of the acceleration of the block.
b) Find the magnitude of the acceleration of the slab.

LB

Laura Bravo

Numerade Educator

Problem 95

As shown in the figure with Problem 4.94 , a block of mass $M_{1}=0.250 \mathrm{~kg}$ is initially at rest on a slab of mass $M_{2}=0.420 \mathrm{~kg}$, and the slab is initially at rest on a level table. A string of negligible mass is connected to the slab, runs over a frictionless pulley on the edge of the table, and is attached to a hanging mass $M_{3}=1.80 \mathrm{~kg} .$ The block rests on the slab but is not tied to the string, so friction provides the only horizontal force on the block. The slab has a coefficient of kinetic friction $\mu_{\mathrm{k}}=0.340$ with both the table and the block. When released, $M_{3}$ pulls on the string, which accelerates the slab so quickly that the block starts to slide on the slab. Before the block slides off the top of the slab:
a) Find the magnitude of the acceleration of the block.
b) Find the magnitude of the acceleration of the slab.

LB

Laura Bravo

Numerade Educator

Problem 95

s shown in the figure with Problem 4.94 , a block of mass $M_{1}=0.250 \mathrm{~kg}$ is initially at rest on a slab of mass $M_{2}=0.420 \mathrm{~kg},$ and the slab is initially at rest on a level table. A string of negligible mass is connected to the slab, runs over a frictionless pulley on the edge of the table, and is attached to a hanging mass $M_{3}=1.80 \mathrm{~kg} .$ The block rests on the slab but is not tied to the string, so friction provides the only horizontal force on the block. The slab has a coefficient of kinetic friction $\mu_{\mathrm{k}}=0.340$ with both the table and the block. When released, $M_{3}$ pulls on the string, which accelerates the slab so quickly that the block starts to slide on the

LB

Laura Bravo

Numerade Educator

Problem 96

Two blocks are connected
by a massless rope, as shown in the figure. Block 1 has mass $m_{1}=1.267 \mathrm{~kg}$, and block 2 has mass $m_{2}=3.557 \mathrm{~kg} .$ The two blocks move on a frictionless, horizontal tabletop. A horizontal external force, $F=12.61 \mathrm{~N}$, acts on block
2. What is the tension in the rope connecting the two blocks?

Sachin Rao

Numerade Educator

Problem 97

Two blocks are connected by a massless rope as shown in the figure. Block 2 has mass $m_{2}=3.577 \mathrm{~kg} .$ The two blocks move on a frictionless, horizontal tabletop. A horizontal external force, $F=13.89 \mathrm{~N}$, acts on block
2. The tension in the rope connecting the two blocks is $4.094 \mathrm{~N}$. What is the mass of block $1 ?$

Sachin Rao

Numerade Educator

Problem 98

Two blocks are connected by a massless rope as shown in the figure. Block 1 has mass $m_{1}=1.725 \mathrm{~kg} .$ The two blocks move on a frictionless, horizontal tabletop. A horizontal external force, $F=15.17 \mathrm{~N}$, acts on block
2. The tension in the rope connecting the two blocks is $4.915 \mathrm{~N}$. What is the mass of block $2 ?$

Sachin Rao

Numerade Educator

Problem 99

Two blocks are connected by a massless rope as shown in the figure. Block 1 has mass $m_{1}=1.955 \mathrm{~kg}$, and block 2 has mass $m_{2}=3.619 \mathrm{~kg} .$ The two blocks move on a frictionless, horizontal tabletop. The tension in the rope connecting the two blocks is $5.777 \mathrm{~N}$. What is the magnitude of the horizontal external force $F$ that is acting on block $2 ?$

Sachin Rao

Numerade Educator

Problem 100

Two blocks are connected by a massless rope as shown in the figure. Block 1 has mass $m_{1}=1.955 \mathrm{~kg}$, and block 2 has mass $m_{2}=3.619 \mathrm{~kg} .$ The two blocks move on a frictionless, horizontal tabletop. The tension in the rope connecting the two blocks is $5.777 \mathrm{~N}$. What is the magnitude of the horizontal external force $F$ that is acting on block $2 ?$

Sachin Rao

Numerade Educator

Problem 101

Two blocks are connected by a massless rope running over two frictionless pulleys, as shown in the figure. Block 1 has mass $m_{1}=1.411 \mathrm{~kg}$ The blocks are released from rest. Block 1 accelerates upward with an acceleration of $4.352 \mathrm{~m} / \mathrm{s}^{2} .$ What is the mass of block $2 ?$

Sachin Rao

Numerade Educator

Problem 102

Two blocks are connected by a massless rope running over two frictionless pulleys, as shown in the figure. Block 2 has mass $m_{2}=3.681 \mathrm{~kg}$ The blocks are released from rest. Block 2 accelerates downward with an acceleration of $3.760 \mathrm{~m} / \mathrm{s}^{2}$. What is the mass of block $1 ?$

Sachin Rao

Numerade Educator

Problem 103

A curling stone of mass $19.00 \mathrm{~kg}$ is released with an initial speed $v_{0}$ and slides on level ice. The coefficient of kinetic friction between the curling stone and the ice is $0.01869 .$ The curling stone travels a distance of $36.01 \mathrm{~m}$ before it stops. What is the initial speed of the curling stone?

Sachin Rao

Numerade Educator

Problem 104

A curling stone of mass $19.00 \mathrm{~kg}$ is released with an initial speed $v_{0}=2.788 \mathrm{~m} / \mathrm{s}$ and slides on level ice. The coefficient of kinetic friction between the curling stone and the ice is $0.01097 .$ How far does the curling stone travel before it stops?

Sachin Rao

Numerade Educator

Problem 105

A curling stone of mass $19.00 \mathrm{~kg}$ is released with an initial speed $v_{0}=3.070 \mathrm{~m} / \mathrm{s}$ and slides on level ice. The curling stone travels $36.21 \mathrm{~m}$ before it stops. What is the coefficient of kinetic friction between the curling stone and the ice?

Sachin Rao

Numerade Educator