College Physics Explore and Apply

Eugenia Etkina; Alan Van Heuvelen; Gorazd Planinši?

Chapter 4 Applying Newton's Laws - all with Video Answers

Educators

Chapter Questions

01:27

Problem 1

Determine the $x$ - and $y$ -components of each force vector shown in FIGURE P4.1 , FIGURE P4.2.

Manish Kumar

Numerade Educator

01:56

Problem 2

Determine the $x$ - and $y$ -components of each force vector shown in Figure P4.2.

Manish Kumar

Numerade Educator

01:19

Problem 3

Determine the $x$ - and $y-$ components of each displacement shown in Figure $P 4.3 .$

Manish Kumar

Numerade Educator

01:36

The $x$ - and $y$ -components of several unknown forces are listed below $\left(F_{x}, F_{y}\right) .$ For each force, draw on an $x, y$ coordinate system the components of the force vectors. Determine the magnitude and direction of each force:
(a) $(+100 \mathrm{N},-100 \mathrm{N})$
(b) $(-300 \mathrm{N},-400 \mathrm{N}),$ and
(c) $(-400 \mathrm{N},+300 \mathrm{N})$.

Manish Kumar

Numerade Educator

01:30

Problem 5

The $x$ - and $y$ -scalar components of several unknown forces are listed below $\left(F_{x}, F_{y}\right) .$ For each force, draw an $x, y$ coordinate system and the vector components of the force vectors. Determine the magnitude and direction of each force:
(a) $(-200 \mathrm{N},+100 \mathrm{N})$
(b) $(+300 \mathrm{N},+400 \mathrm{N})$ and
(c) $(+400 \mathrm{N},-300 \mathrm{N})$

Manish Kumar

Numerade Educator

00:58

Problem 6

Three ropes pull on a knot shown in Figure $P 4.6$ a. The knot is not accelerating. A partially completed force diagram for the knot is shown in Figure P4.6b. Use qualitative reasoning to determine the magnitudes of the forces that ropes 2 and 3 exert on the knot. Explain in words how you arrived at your answer.

Manish Kumar

Numerade Educator

03:39

Problem 7

Figure $P 4.7$ shows an unlabeled force diagram for a hockey puck. The length of the sides of the square grid corresponds to a force magnitude of $1 \mathrm{N}$. Draw a similar square grid on paper and then draw the vector for the force that should be exerted on the puck so that the puck (a) moves with constant speed, (b) moves with constant acceleration toward the north, (c) moves with constant acceleration toward the west, and (d) moves with constant acceleration toward the east.

Manish Kumar

Numerade Educator

03:20

Problem 8

For each of the following situations, draw the forces exerted on the moving object and identify the other object causing each force. (a) You pull a wagon along a level floor using a rope oriented $45^{\circ}$ above the horizontal. (b) A bus moving on a horizontal road slows in order to stop. (c) You slide down an inclined waterslide. (d) You lift your overnight bag into the overhead compartment on an airplane. (e) A rope connects two boxes on a horizontal floor, and you pull horizontally on a second rope attached to the right side of the right box (consider each box separately).

Manish Kumar

Numerade Educator

09:34

Problem 9

Write Newton's second law in component form for each of the situations described in Problem $4.8 .$

Manish Kumar

Numerade Educator

03:08

Problem 10

For the situations described here, construct a force diagram for the block, sled, and skydiver. (a) A cinder block sits on the ground.
(b) A rope pulls at an angle of $30^{\circ}$ relative to the horizontal on a sled moving on a horizontal surface. The sled moves at increasing speed toward the right (the surface is not smooth.) (c) A rope pulls on a sled parallel to an inclined slope (inclined at an arbitrary angle). The sled moves at increasing speed up the slope. (d) A skydiver falls downward at constant terminal velocity (air resistance is present).

Manish Kumar

Numerade Educator

04:06

Problem 11

Write Newton's second law in component form for each of the situations described in Problem 4.10 .

Manish Kumar

Numerade Educator

01:21

Problem 12

Apply Newton's second law in component form for the force diagram shown in Figure $\mathrm{P} 4.1$.

Manish Kumar

Numerade Educator

01:12

Problem 13

Apply Newton's second law in component form for the force diagram shown in Figure $\mathrm{P} 4.2$.

Manish Kumar

Numerade Educator

04:14

Problem 14

The three sets of equations below are the horizontal $x$ - and vertical $y$ -component forms of Newton's second law applied to three physical processes. For each case, solve for the unknowns. Then work backward and construct a force diagram for the object of interest and invent a problem for which the equations could be an answer (there are many possibilities). Note the difference between $\mathrm{N}$ (unit of force, newton) and $N$ (the symbol for the normal force).
(a)
$\begin{aligned}(5.0 \mathrm{kg}) a_{x}=&(50 \mathrm{N}) \cos 30^{\circ}+N \cos 90^{\circ} \\ &+(5.0 \mathrm{kg})(9.8 \mathrm{N} / \mathrm{kg}) \cos 90^{\circ} \\(5.0 \mathrm{kg}) 0=&(-50 \mathrm{N}) \sin 30^{\circ}+N \sin 90^{\circ} \\ &-(5.0 \mathrm{kg})(9.8 \mathrm{N} / \mathrm{kg}) \sin 90^{\circ} \end{aligned}$
(b) This process involves an object on an incline.
$\begin{aligned}(5.0 \mathrm{kg}) a_{x}=&(30 \mathrm{N}) \cos 30^{\circ}+N \cos 90^{\circ} \\ &-(5.0 \mathrm{kg})(9.8 \mathrm{N} / \mathrm{kg}) \cos 60^{\circ} \\(5.0 \mathrm{kg}) 0=&(30 \mathrm{N}) \sin 30^{\circ}+N \sin 90^{\circ} \\ &-(5.0 \mathrm{kg})(9.8 \mathrm{N} / \mathrm{kg}) \sin 60^{\circ} \end{aligned}$
(c)
$(5.0 \mathrm{kg}) a_{x}=(50 \mathrm{N}) \cos 30^{\circ}+N \cos 90^{\circ}$
$$
\begin{aligned}(5.0 \mathrm{kg}) 0=&(5.0 \mathrm{kg})(9.8 \mathrm{N} / \mathrm{kg}) \cos 90^{\circ} \\ &-(5.0 \mathrm{kg})(9.8 \mathrm{N} / \mathrm{kg}) \sin 90^{\circ} \end{aligned}
$$
$x-0=(2.0 \mathrm{m} / \mathrm{s})(4.0 \mathrm{s})+\frac{1}{2} a_{x}(4.0 \mathrm{s})^{2}$
Provide all the information you know about your process.

Supratim Pal

Numerade Educator

03:19

Problem 15

You exert a force of $100 \mathrm{N}$ on a rope that pulls a sled across a very smooth surface. The rope is oriented $37^{\circ}$ above the horizontal. The sled and its occupant have a total mass of $40 \mathrm{kg} .$ The sled starts at rest and moves $10 \mathrm{m} .$ List all the quantities you can determine using these givens and determine three of the quantities on the list.

Manish Kumar

Numerade Educator

01:46

Problem 16

You exert a force of a known magnitude $F$ on a grocery cart of total mass $m .$ The force you exert on the cart points at an angle $\theta$ below the horizontal. If the cart starts at rest, determine an expression for the speed of the cart after it travels a distance $d$. Ignore friction.

Manish Kumar

Numerade Educator

01:24

Problem 17

At the start of his race, $86-\mathrm{kg}$ Olympic $100-\mathrm{m}$ champion Usain Bolt from Jamaica pushes against the starting block, exerting an average force of $1700 \mathrm{N}$. The force that the block exerts on his foot points $20^{\circ}$ above the horizontal. Determine his horizontal speed after the force is exerted for 0.32 s. Indicate any assumptions you made.

Manish Kumar

Numerade Educator

03:06

Problem 18

A train has an acceleration of magnitude $1.4 \mathrm{m} / \mathrm{s}^{2}$ while stopping. A pendulum with a $0.50-\mathrm{kg}$ bob is attached to a ceiling of one of the cars. Determine everything you can about the pendulum during the deceleration of the train.

Manish Kumar

Numerade Educator

04:16

Problem 19

Finn and Hazel are using a battery-powered fan fixed on a low-friction cart. As the fan blades rotate, they exert a force on the air and therefore the air exerts an equal and opposite force on the blades, causing the cart to move at constant acceleration. They decide to investigate how the acceleration of the cart depends on the tilt of the fan. They conduct two experiments: one with the fan oriented horizontally (see Figure $\mathbf{P 4 . 1 9 a}$ ) and one by tilting the axis of the fan by a certain angle (Figure $\mathrm{P} 4.19 \mathrm{b}$ ). In both experiments, they hold the cart still, turn on the fan, then let the cart move for some time before stopping the cart. During the experiment they measure the acceleration of the cart using a motion detector. The graphs in Figure P4.19c show their measurements. (a) Which graph (A or B) belongs to the cart with the horizontal fan and which to the cart with the tilted fan? Explain. (b) Based on the graph, estimate the angle between the axis of the fan and the horizontal in the second experiment. Indicate any assumptions that you made. Check how your result compares with the angle on the photo (Figure $\mathrm{P} 4.19 \mathrm{c}$ ) of the actual experimental setup (you will need a protractor). Indicate any assumptions that you made.

Manish Kumar

Numerade Educator

00:43

Problem 20

A 91.0 -kg refrigerator sits on the floor. The coefficient of static friction between the refrigerator and the floor is $0.60 .$ What is the minimum force that one needs to exert on the refrigerator to start the refrigerator sliding?

Manish Kumar

Numerade Educator

00:35

Problem 21

A $60-\mathrm{kg}$ student sitting on a hardwood floor does not slide until pulled by a 240-N horizontal force. Determine the coefficient of static friction between the student and floor.

Manish Kumar

Numerade Educator

02:40

Problem 22

A car traveling at $60 \mathrm{mi} / \mathrm{h}(97 \mathrm{km} / \mathrm{h})$ can stop in $48 \mathrm{m}$ on a level road. Determine the coefficient of friction between the tires and the road. Assume that the car starts skidding the moment the driver hits the brakes. Is this kinetic or static friction? Explain.

Manish Kumar

Numerade Educator

01:41

Problem 23

A $50-\mathrm{kg}$ box rests on the floor. The coefficients of static and kinetic friction between the bottom of the box and the floor are 0.70 and 0.50 , respectively. (a) What is the minimum force a person needs to exert on the box to start it sliding? (b) After the box starts sliding, the person continues to push it, exerting the same force. What is the acceleration of the box?

Manish Kumar

Numerade Educator

03:11

Problem 24

Marsha is pushing down and to the right on a $12-\mathrm{kg}$ box at an angle of $30^{\circ}$ below horizontal. The box slides at constant velocity across a carpet whose coefficient of kinetic friction with the box is 0.70. Determine three physical quantities using this information, one of which is a kinematics quantity.

Manish Kumar

Numerade Educator

03:10

Problem 25

You want to determine the coefficient of kinetic friction between a $1 \mathrm{m} \times 1 \mathrm{m}$ rug and a wooden floor. You obtain a piece of the same rug of size $10 \mathrm{cm} \times 10 \mathrm{cm}$ (which has a surface area 100 times smaller than the entire rug), a scale for measuring mass, a force meter, and an object of mass $m_{0}$. Which of the following procedures would you choose to obtain the correct value of kinetic friction between the rug and the floor?
(a) Put the object on the piece of rug. Measure the force $F_{\mathrm{H} \text { on } \mathrm{RP}}$ exerted
by the hand on the rug piece in the horizontal direction while moving it with constant speed along the wooden floor. Calculate the coefficient of kinetic friction as $\mu_{\mathrm{k}}=\frac{F_{\mathrm{H}} \text { on } \mathrm{RP}}{m_{\mathrm{O}} g}$
(b) Use the same method described in (a) but calculate the coefficient of friction as $\mu_{\mathrm{k}}=\frac{100 \cdot F_{\mathrm{H} \text { on } \mathrm{RP}}}{m_{\mathrm{O}} g}$
(c) Use the same method described in (a) but also measure the mass of the rug piece $m_{\mathrm{RP}}$ and calculate the coefficient of friction as $\mu_{\mathrm{k}}=\frac{F_{\mathrm{H} \text { on } \mathrm{RP}}}{\left(m_{\mathrm{O}}+m_{\mathrm{RP}}\right) g}$
(d) Use the same method described in (c) but calculate the coefficient of friction as $\mu_{\mathrm{k}}=\frac{100 \cdot F_{\mathrm{H} \text { on } \mathrm{RP}}}{\left(m_{\mathrm{O}}+m_{\mathrm{RP}}\right) g}$

Manish Kumar

Numerade Educator

01:03

Problem 26

A wagon is accelerating to the right. A book is placed against the interior back wall of the wagon and does not slide down (see Figure $P 4.26$ ). Explain how this can be.

Manish Kumar

Numerade Educator

01:19

Problem 27

In Problem 4.26, the coefficient of static friction between the book and the vertical back of the wagon is $\mu_{\mathrm{s}} .$ Determine an expression for the minimum acceleration of the wagon in terms of $\mu_{\mathrm{s}}$ so that the book does not slide down. Does the mass of the book matter? Explain.

Manish Kumar

Numerade Educator

02:31

Problem 28

A car has a mass of 1520 kg. While traveling at $20 \mathrm{m} / \mathrm{s}$, the driver applies the brakes to stop the car on a wet surface with a 0.40 coefficient of friction. (a) How far does the car travel before stopping? (b) If a different car with a mass 1.5 times greater is on the road traveling at the same speed and the coefficient of friction between the road and the tires is the same, what will its stopping distance be? Explain your results.

Manish Kumar

Numerade Educator

03:42

Problem 29

A 20 -kg wagon accelerates on a horizontal surface at $0.50 \mathrm{m} / \mathrm{s}^{2}$ when pulled by a rope exerting a $120-\mathrm{N}$ force on the wagon at an angle of $25^{\circ}$ above the horizontal. Determine the magnitude of the effective friction force exerted on the wagon and the effective coefficient of friction associated with this force.

Manish Kumar

Numerade Educator

02:47

Problem 30

A crate of mass $m$ sitting on a horizontal floor is attached to a rope that pulls at an angle $\theta$ above the horizontal. The coefficient of static friction between the crate and floor is $\mu_{\mathrm{s}}$. (a) Construct a force diagram for the crate when being pulled by the rope but not sliding. (b) Determine an expression for the smallest force that the rope needs to exert on the crate that will cause the crate to start sliding.

Manish Kumar

Numerade Educator

02:26

Problem 31

You absentmindedly leave your book bag on the top of your car. Estimate the safe acceleration of the car needed for the bag to stay on the roof. Describe the assumptions that you made.

Manish Kumar

Numerade Educator

01:23

Problem 32

Block 1 is on a horizontal surface with a 0.29 coefficient of kinetic friction between it and the surface. A string attached to the front of block 1 passes over a light frictionless pulley and down to hanging block 2 . Determine the mass of block 2 in terms of block 1 so that the blocks
move at constant nonzero speed while sliding.

Manish Kumar

Numerade Educator

03:49

Problem 33

You want to use a rope to pull a $10-\mathrm{kg}$ box of books up a plane inclined $30^{\circ}$ above the horizontal. The coefficient of kinetic friction is 0.30 . What force do you need to exert on the other end of the rope if you want to pull the box (a) at constant speed and (b) with a constant acceleration of $0.50 \mathrm{m} / \mathrm{s}^{2}$ up the plane? The rope pulls parallel to the incline.

Manish Kumar

Numerade Educator

02:12

Problem 34

A car with its wheels locked rests on a flatbed of a tow truck. The flatbed's angle with the horizontal is slowly increased. When the angle becomes $40^{\circ},$ the car starts to slide. Determine the coefficient of static friction between the flatbed and the car's tires.

Manish Kumar

Numerade Educator

02:48

Problem 35

Olympic skier Tina Maze skis down a steep slope that descends at an angle of $30^{\circ}$ below the horizontal. The coefficient of sliding friction between her skis and the snow is 0.10. Determine Maze's acceleration, and her speed 6.0 s after starting.

Manish Kumar

Numerade Educator

02:12

Problem 36

Bode Miller, 80-kg downhill skier, descends a slope inclined at $20^{\circ} .$ Determine his acceleration if the coefficient of friction is 0.10. How would this acceleration compare to that of a $160-\mathrm{kg}$ skier going down the same hill? Justify your answer using sound physics reasoning.

Manish Kumar

Numerade Educator

02:43

Problem 37

A book slides off a desk that is tilted $15^{\circ}$ relative to the horizontal. What information about the book or the desk does this number provide?

Manish Kumar

Numerade Educator

04:14

Problem 38

The two sets of equations below are the horizontal $x-$ and vertical $y$ -component forms of Newton's second law applied to two physical processes. In both cases, solve for the unknowns. Then work backward and construct a force diagram for the object of interest and invent a problem for which the equations could be an answer (there are many possibilities). Note the difference between $\mathrm{N}$ (unit of force, newton) and $N$ (symbol for a normal force).
$\begin{aligned}(5.0 \mathrm{kg}) a_{x}=&(50 \mathrm{N}) \cos 30^{\circ}+N \cos 90^{\circ}-0.5 N \cos 0^{\circ} \\ &+(5.0 \mathrm{kg})(9.8 \mathrm{N} / \mathrm{kg}) \cos 90^{\circ} \\(5.0 \mathrm{kg}) 0=&(-50 \mathrm{N}) \sin 30^{\circ}+N \sin 90^{\circ}+0.5 N \sin 0^{\circ} \\ &-(5.0 \mathrm{kg})(9.8 \mathrm{N} / \mathrm{kg}) \sin 90^{\circ} \end{aligned}$
(b) This process involves an object on an incline.
$\begin{aligned}(5.0 \mathrm{kg}) 0=&+F \cos 0^{\circ}+N \cos 90^{\circ}-0.50 N \cos 0^{\circ} \\ &-(5.0 \mathrm{kg})(9.8 \mathrm{N} / \mathrm{kg}) \cos 60^{\circ} \\(5.0 \mathrm{kg}) 0=&+F \sin 0^{\circ}+N \sin 90^{\circ}-0.50 N \sin 0^{\circ} \\ &-(5.0 \mathrm{kg})(9.8 \mathrm{N} / \mathrm{kg}) \sin 60^{\circ} \end{aligned}$

Supratim Pal

Numerade Educator

05:21

Problem 39

Helge, Steve, and Heidi are sitting on a sled on a slope covered with a hard snow. The sled is stationary. The friends have different suggestions for how to make the sled start moving:
Helge: If one of us gets off, the sled will start moving. Steve: We should invite another person to join us, and then the sled will start moving. Heidi: We should get off the sled, polish the bottom of the sled to make it smoother, and sit back down on it. The sled will then start moving. Comment on the students' suggestions and decide whose reasoning is correct. Explain using physics concepts, including appropriate diagrams, why those who were incorrect said what they did, and indicate what part of their reasoning was correct.

Manish Kumar

Numerade Educator

06:46

Problem 40

When traveling on an airplane you get meals on a serving tray that has large coefficients of static and kinetic friction between the tray and dishes on it. For each case below, draw a force diagram for a cup on a serving tray as seen by a stationary observer on Earth and assuming the airplane is moving from left to right. Assume also that the tray is parallel to the velocity of the airplane.
(a) The airplane is flying horizontally at constant speed; the cup is at rest on the tray.
(b) The airplane is on a runway and slowing down; the cup is at rest on the tray.
(c) The airplane is on a runway and slowing down; the cup is sliding. Next to the force diagram draw an arrow that shows the velocity of the cup relative to the airplane.
(d) The airplane is on a runway and speeding up; the cup is at rest on the tray.
(e) The airplane is descending at constant speed at an angle $30^{\circ}$ with respect to horizontal; the cup is at rest on the tray.
(f) The airplane is slowing down and descending at an angle $30^{\circ}$ with respect to horizontal; the cup is at rest on the tray.

Vipender Yadav

Numerade Educator

02:45

Problem 41

A 52 -kg skier starts at rest and slides 30 m down a hill inclined at $12^{\circ}$ relative to the horizontal. List five quantities that describe the motion of the skier, and solve for three of them (at least one should be a kinematics quantity).

Manish Kumar

Numerade Educator

01:35

Problem 42

You agree to build a backyard rope tow to pull your siblings up a $20-\mathrm{m}$ slope that is tilted at $15^{\circ}$ relative to the horizontal. You must choose a motor that can pull your $40-\mathrm{kg}$ sister up the hill. Determine the force that the rope should exert on your sister to pull her up the hill at constant velocity.

Manish Kumar

Numerade Educator

02:27

Problem 43

A soapbox derby racecar starts at rest at the top of a $301-\mathrm{m}$ -long track tilted at an average $4.8^{\circ}$ relative to the horizontal. If the car's speed were not reduced by any structural effects or by friction, how long would it take to complete the race? What is the speed of the car at the end of the race?

Manish Kumar

Numerade Educator

05:18

Problem 44

A person is pushing two carts that are connected with a metal bar so that the carts are moving at constant acceleration $0.2 \mathrm{m} / \mathrm{s}^{2} .$ The masses of the carts are $100 \mathrm{kg}$ and $180 \mathrm{kg},$ and the mass of the connecting bar is $60 \mathrm{kg} .$ Determine (a) the force that the bar exerts on the smaller cart and (b) the force that the bigger cart exerts on the bar. Assume that the friction forces are negligible.

Manish Kumar

Numerade Educator

02:10

Problem 45

A car sitting at rest is hit from the rear by a semi-trailer truck moving at $13 \mathrm{m} / \mathrm{s}$. The car lurches forward with an acceleration of about $300 \mathrm{m} / \mathrm{s}^{2} .$ Figure $\mathrm{P} 4.45$ shows an arrow that represents the force that the neck muscle exerts on the head so that it accelerates forward with the body instead of flipping backward. If the head has a mass of 4.5 kg, what is the horizontal component of the force $\vec{F}$ required to cause this head acceleration? If $\vec{F}$ is directed $37^{\circ}$ below the horizontal, what is the magnitude of $\vec{F} ?$

Supratim Pal

Numerade Educator

03:22

Problem 46

The dogs of four-time Iditarod Trail Sled Dog Race champion Jeff King pull two $100-\mathrm{kg}$ sleds that are connected by a rope. The sleds move on an icy surface. The dogs exert a $240-\mathrm{N}$ force on the rope attached to the front sled. Find the acceleration of the sleds and the force the rope between the sleds exerts on each sled. The front rope pulls horizontally.

Manish Kumar

Numerade Educator

03:07

Problem 47

You pull a rope oriented at a $37^{\circ}$ angle above the horizontal. The other end of the rope is attached to the front of the first of two wagons that have the same 30 -kg mass. The rope exerts a force of magnitude $T_{1}$ on the first wagon. The wagons are connected by a second horizontal rope that exerts a force of magnitude $T_{2}$ on the second wagon. Determine the magnitudes of $T_{1}$ and $T_{2}$ if the acceleration of the wagons is $2.0 \mathrm{m} / \mathrm{s}^{2}$.

Manish Kumar

Numerade Educator

03:56

Problem 48

Rope 1 pulls horizontally, exerting a force of $45 \mathrm{N}$ on an 18 -kg wagon attached by a second horizontal rope to a second 12 -kg wagon. Make a list of physical quantities you can determine using this information, and solve for three of them, including one kinematics quantity.

Manish Kumar

Numerade Educator

05:23

Problem 49

Three sleds of masses $m_{1}, m_{2}, m_{3}$ are on a smooth horizontal surface (ice) and connected by ropes, so that if you pull the rope connected to sled $1,$ all the sleds start moving. Imagine that you exert a force of a known magnitude on the rope attached to the first sled. What will happen to all of the sleds? Provide information about their accelerations and all the forces exerted on them. What assumptions did you make?

Manish Kumar

Numerade Educator

05:04

Problem 50

Repeat Problem 4.49, only this time with the sleds on a slope inclined at $\theta$.

Manish Kumar

Numerade Educator

03:43

Problem 51

A skier is moving down a snowy hill with an acceleration of $0.4 \mathrm{m} / \mathrm{s}^{2}$. The angle of the slope is $5^{\circ}$ to the horizontal. What is the acceleration of the same skier when she is moving down a hill with a slope of $10^{\circ}$ ? Assume the coefficient of kinetic friction is the same in both cases.

Manish Kumar

Numerade Educator

04:25

Problem 52

A person holds a $200-\mathrm{g}$ block that is connected to a $250-\mathrm{g}$ block by a string going over a light pulley with no friction in the bearing (an Atwood machine). After the person releases the $200-\mathrm{g}$ block, it starts moving upward and the heavier block descends. (a) What is the acceleration of each block? (b) What is the force that the string exerts on each block? (c) How long will it take each block to traverse $1.0 \mathrm{m} ?$

Manish Kumar

Numerade Educator

02:08

Problem 53

Two blocks of masses $m_{1}$ and $m_{2}$ are connected to each other on an Atwood machine. A person holds one of the blocks with her hand. When the system is released, the heavier block moves down with an acceleration of $2.3 \mathrm{m} / \mathrm{s}^{2}$ and the lighter object moves up with an acceleration of the same magnitude. What is one possible set of masses for the blocks?

Manish Kumar

Numerade Educator

02:17

Problem 54

The 20 -kg block shown in Figure $P 4.54$ accelerates down and to the left, and the 10 -kg block accelerates up. Find the magnitude of this acceleration and the force that the cable exerts on a block. There is no friction between the block and the inclined plane, and the pulley is frictionless and light.

Manish Kumar

Numerade Educator

03:24

Problem 55

A squirrel jumps off a roof in the horizontal direction. The origin of the coordinate system is at the point where the squirrel leaves the roof. Complete Table $\mathrm{P} 4.55$ by drawing crosses in the cells that correctly connect the physical quantities in the first column that describe the motion of the squirrel and the descriptions of what is happening to these quantities while the squirrel is in flight. Consider the squirrel as a point-like object and assume that the resistive force exerted by the air is negligible.

Manish Kumar

Numerade Educator

03:19

Problem 56

A frog jumps at an angle $30^{\circ}$ above the horizontal. The origin of the coordinate system is at the point where the frog leaves the ground. Complete Table P4.55 by drawing check marks in the cells that correctly connect the quantities in the first column that describe the motion of the frog and the descriptions of what is happening to these quantities while the frog is moving. Consider the frog as a point-like object and assume that the resistive force exerted by the air is negligible.

Manish Kumar

Numerade Educator

01:20

Problem 57

A bowling ball rolls off a table. Draw a force diagram for the ball when on the table and when in the air at two different positions.

Manish Kumar

Numerade Educator

07:56

Problem 58

A tennis ball is served from the back line of the court such that it leaves the racket $2.4 \mathrm{m}$ above the ground in a horizontal direction at a speed of $22.3 \mathrm{m} / \mathrm{s}(50 \mathrm{mi} / \mathrm{h}) .$ (a) Will the ball cross a $0.91-\mathrm{m}$ -high net $11.9 \mathrm{m}$ in front of the server? (b) Will the ball land in the service court, which is within $6.4 \mathrm{m}$ of the net on the other side of the net?

Manish Kumar

Numerade Educator

01:49

Problem 59

The equations below describe a projectile's path. Solve for the unknowns and then invent a process that the equations might describe. There are many possibilities.
$$
\begin{array}{l}
x=0+(20 \mathrm{m} / \mathrm{s})\left(\cos 0^{\circ}\right) t \\
0=8.0 \mathrm{m}+(20 \mathrm{m} / \mathrm{s})\left(\sin 0^{\circ}\right) t-\frac{1}{2}\left(9.8 \mathrm{m} / \mathrm{s}^{2}\right) t^{2}
\end{array}
$$

Manish Kumar

Numerade Educator

05:24

Problem 60

An airplane is delivering food to a small island. It flies $100 \mathrm{m}$ above the ground at a speed of $160 \mathrm{m} / \mathrm{s}$. (a) Where should the parcel be released so it lands on the island? Neglect air resistance. (b) Estimate whether you should release the parcel earlier or later if there is air resistance. Explain.

Manish Kumar

Numerade Educator

00:51

Problem 61

A ball moves in an arc through the air (see Figure $P 4.61$ ). Construct a force diagram for the ball when at positions (a), (b), and (c). Ignore the resistive force exerted by the air on the ball.

Manish Kumar

Numerade Educator

01:28

Problem 62

A marble is thrown as a projectile at an angle above the horizontal. Draw its path during the flight. Choose six different positions along the path so that one of them is at the highest point. For each position, indicate the direction of the marble's velocity, acceleration, and all of the forces exerted on it by other objects. Ignore the resistive force exerted by the air on the marble.

Manish Kumar

Numerade Educator

04:39

Problem 63

Marbles are exiting a container through a horizontal nozzle positioned $1.3 \mathrm{m}$ above sandy ground (see Figure $P 4.63$ ). You notice that all the marbles land between $0.25 \mathrm{m}$ and $0.45 \mathrm{m}$ from the point directly below the end of the nozzle. How do you explain this observation? What can you determine based on the data given in the problem? Indicate any assumptions that you made.

Manish Kumar

Numerade Educator

05:07

Problem 64

On May $20,1999,$ Robbie Knievel easily cleared a narrow part of the Grand Canyon during a world-record-setting long-distance motorcycle jump $-69.5 \mathrm{m} .$ He left the jump ramp at a $10^{\circ}$ angle above the horizontal. How fast was he traveling when he left the ramp? Indicate any assumptions you made.

Manish Kumar

Numerade Educator

04:24

Problem 65

Daring Darless wishes to cross the Grand Canyon of the Snake River by being shot from a cannon. She wishes to be launched at $60^{\circ}$ relative to the horizontal so she can spend more time in the air waving to the crowd. With what minimum speed must she be launched to cross the $520-\mathrm{m}$ gap?

Manish Kumar

Numerade Educator

04:16

Problem 66

A football punter wants to kick the ball so that it is in the air for $4.0 \mathrm{s}$ and lands $50 \mathrm{m}$ from where it was kicked. At what angle and with what initial speed should he kick the ball? Assume that the ball leaves $1.0 \mathrm{m}$ above the ground.

Manish Kumar

Numerade Educator

01:59

Problem 67

If you shoot a cannonball from the same cannon first at $30^{\circ}$ and then at $60^{\circ}$ relative to the horizontal, which orientation of the cannon will make the ball go farther? How do you know? Under what circumstances is your answer valid? Explain.

Manish Kumar

Numerade Educator

00:48

Problem 68

When you actually perform the experiment described in Problem $4.67,$ the ball shot at a $60^{\circ}$ angle lands closer to the cannon than the ball shot at a $30^{\circ}$ angle. Explain why this happens.

Manish Kumar

Numerade Educator

06:53

Problem 69

You can shoot an arrow straight up so that it reaches the top of a $25-\mathrm{m}$ -tall building. (a) How far will the arrow travel if you shoot it horizontally while pulling the bow in the same way? The arrow starts $1.45 \mathrm{m}$ above the ground. (b) Where do you need to put a target that is $1.45 \mathrm{m}$ above the ground in order to hit it if you aim $30^{\circ}$ above the horizontal? (c) What assumptions did you make?

Manish Kumar

Numerade Educator

02:17

Problem 70

Robin Hood wishes to split an arrow already in the bull's-eye of a target $40 \mathrm{m}$ away. If he aims directly at the arrow, by how much will he miss? The arrow leaves the bow horizontally at $40 \mathrm{m} / \mathrm{s}$.

Manish Kumar

Numerade Educator

02:09

Problem 71

Three force diagrams for a car on a road are shown in Figure $P 4.71$. Indicate as many situations as possible for the car in terms of its velocity and acceleration at that instant for each diagram.

Manish Kumar

Numerade Educator

01:20

Problem 72

A minivan of mass $1560 \mathrm{kg}$ starts at rest and then accelerates at $2.0 \mathrm{m} / \mathrm{s}^{2}$. (a) What is the object exerting the force on the minivan that causes it to accelerate? What type of force is it? (b) Air resistance and other opposing resistive forces are 300 N. Determine the magnitude of the force that causes the minivan to accelerate in the forward direction.

Manish Kumar

Numerade Educator

05:20

Problem 73

A daredevil motorcycle rider hires you to plan the details for a stunt in which she will fly her motorcycle over six school buses. Assume the ride starts on flat ground. Provide as much information as you can to help the rider successfully complete the stunt.

Manish Kumar

Numerade Educator

04:03

Problem 74

Emily pulls a 5 -kg block across a rough horizontal surface, exerting a constant force on the block. The magnitude of the force is initially $5 \mathrm{N}$, and the block moves at a constant velocity of $2 \mathrm{m} / \mathrm{s} .$ While the block is moving, Emily instantly increases the force to $10 \mathrm{N}$. How will the block move now? Andrew says: The block will move at a constant velocity of $4 \mathrm{m} / \mathrm{s}$ because it was initially moving with constant velocity and the final force is two times larger than the initial force. Jasit says: The block will move at a constant acceleration of $2 \mathrm{m} / \mathrm{s}^{2}$ because the sum of the forces exerted on the block is $10 \mathrm{N}$ and the mass of the block is $5 \mathrm{kg}$ Mary says: The block will move at a constant acceleration of $1 \mathrm{m} / \mathrm{s}^{2}$ because the sum of the forces exerted on the block is $5 \mathrm{N}$ and the mass of the block is $5 \mathrm{kg}$. Explain which student is correct. Also comment on what is incorrect about the other statements.

Manish Kumar

Numerade Educator

03:20

Problem 75

You abruptly push a $1.7-\mathrm{kg}$ book along a table and let go. The book comes to a stop after a short distance. Figure $\mathrm{P} 4.75$ shows the accelerationversus-time graph of the book as recorded by a motion detector. Estimate the following quantities: (a) the coefficient of kinetic friction between the book and the table and (b) the maximum force exerted by your hand on the book.

Manish Kumar

Numerade Educator

05:27

Problem 76

In the situation of Problem 4.75, estimate (a) the maximum speed of the book and (b) the clock reading when your hand stopped exerting the force on the book.

Manish Kumar

Numerade Educator

03:03

Problem 77

Estimate the range of the horizontal force that a sidewalk exerts on you during every step while you are walking. Indicate clearly how you made the estimate.

Manish Kumar

Numerade Educator

03:15

Problem 78

Two blocks of masses $m_{1}$ and $m_{2}$ hang at the ends of a string that passes over the very light pulley with low friction bearings shown in Figure $\mathbf{P 4 . 7 8}$. Determine an expression in terms of the masses and any other needed quantities for the magnitude of the acceleration of each block and the force that the string exerts on each block. Apply the equation for two cases: (a) the blocks have the same mass, but one is positioned lower than the other and (b) the blocks have different masses, but the heavier block is positioned higher than the light one. What assumptions did you make?

Massimo Antonelli

Numerade Educator

03:23

Problem 79

A 3.5-kg object placed on an inclined plane (angle $30^{\circ}$ above the horizontal) is connected by a string going over a pulley to a 1.0 -kg hanging block. (a) Determine the acceleration of the system if there is no friction between the object and the surface of the inclined plane. (b) Determine the magnitude of the force that the string exerts on both objects.

Manish Kumar

Numerade Educator

06:14

Problem 80

A $3.5-\mathrm{kg}$ object placed on an inclined plane (angle $30^{\circ}$ above the horizontal) is connected by a string going over a pulley to a 1.0 -kg object. Determine the acceleration of the system if the coefficient of static friction between object 1 and the surface of the inclined plane is 0.30 and equals the coefficient of kinetic friction.

Manish Kumar

Numerade Educator

06:28

Problem 81

An object of mass $m_{1}$ placed on an inclined plane (angle $\theta$ above the horizontal) is connected by a string going over a pulley to a hanging object of mass $m_{2} .$ Determine the acceleration of the system if the coefficient of static friction between object 1 and the surface of the inclined plane is $\mu_{\mathrm{s}}$ and the coefficient of kinetic friction is $\mu_{\mathrm{k}} .$ If the problem has multiple answers, explore all of them.

Manish Kumar

Numerade Educator

10:35

Problem 82

You are driving at a reasonable constant velocity in a van with a wind shield tilted $120^{\circ}$ relative to the horizontal (see Figure $\mathbf{P} 4.82$ ). As you pass under a utility worker fixing a power line, his wallet falls onto the windshield. Determine the acceleration needed by the van so that the wallet stays in place. When choosing your coordinate axes, remember that you want the wallet's acceleration to be horizontal rather than vertical. What assumptions and approximations did you make?

Alexander Allen

Numerade Educator

03:40

Problem 83

Figure P4.19c (from Problem 4.19 above) shows acceleration- versus-time graphs for two fan carts. For each cart, estimate (a) the final velocity of the cart and (b) the distance traveled by the cart while it was speeding up. In both experiments the cart started to move from rest. Indicate any assumptions that you made.

Supratim Pal

Numerade Educator

02:37

Problem 84

In the situation of Problem 2.71 (Chapter 2 ) and using the data in the accompanying table, determine the coefficient of kinetic friction between Piglet and the wooden floor.

Anurag Kumar

Numerade Educator

01:54

Problem 85

You push a small box so that it starts moving with a speed of $1 \mathrm{m} / \mathrm{s}$ along a rough table. After $1 \mathrm{m},$ the box reaches the edge of the table and lands on the floor $20 \mathrm{cm}$ from the table edge. The surface of the table is $0.8 \mathrm{m}$ above the floor. Determine (a) the coefficient of friction between the box and the table and (b) the speed of the box at the moment it hits the floor.

Narayan Hari

Numerade Educator

01:42

Problem 86

Debbie wants to determine the initial speed at which a spring toy shoots a marble. She assumes the toy shoots the marble with the same speed every time. She shoots the marble horizontally from different heights, using different numbers of bricks with equal heights of $20 \mathrm{cm}$ on a table as a support (see Figure $P 4.86$ ). In every experiment she records the number of bricks and the distance $D$ from the table the marble lands (see the table at right). When she finishes collecting the data, she realizes that she has forgotten to measure the distance between the surface of the table and the floor, $h$. Determine the initial speed of the marble and the distance $h$ using Debbie's data. (Hint: This problem requires linearization. First, express distance $D$ as a function of initial speed of the marble and the height from which the marble is shot. Then rearrange the equation to obtain linear dependence on the height, plot the best-fit line, and determine unknown quantities from the data that you obtained from the graph.)

Dominador Tan

Numerade Educator

03:56

Problem 87

Your friend has a pie on the roof of his van. You are standing on the ground and observe the van stopping abruptly for a red light. The pie does not slip off the roof. (a) Construct a motion diagram and a force diagram for the pie as the van approaches the red light, from your frame of reference and from the driver's frame of reference. (b) Repeat part (a) for the case when the light turns green. Be sure to specify the observer and identify the other object causing each force. (c) Are the motion diagrams consistent with the force diagrams for each case?

Manish Kumar

Numerade Educator

01:55

Problem 88

A ledge on a building is $20 \mathrm{m}$ above the ground. A taut rope attached to a $4.0-\mathrm{kg}$ can of paint sitting on the ledge passes up over a pulley and straight down to a 3.0 -kg can of nails on the ground. If the can of paint is accidentally knocked off the ledge, what time interval does a carpenter have to catch the can of paint before it smashes on the ground?

Manish Kumar

Numerade Educator

02:00

Problem 89

You are hired to devise a method to determine the coefficient of friction between the ground and the soles of a shoe and of its competitors. Explain your experimental technique and provide a physics analysis that could be used by others using this method.

Manish Kumar

Numerade Educator

01:26

Problem 90

The mass of a spacecraft is about 480 kg. An engine designed to increase the speed of the spacecraft while in outer space provides $0.09-\mathrm{N}$ thrust at maximum power. By how much does the engine cause the craft's speed to change in 1 week of running at maximum power? Describe any assumptions you made.

Manish Kumar

Numerade Educator

04:23

Problem 91

A $60-\mathrm{kg}$ Rollerblader rolls $10 \mathrm{m}$ down a $30^{\circ}$ incline. When she reaches the level floor at the bottom, she applies the brakes. Use Newton's second law to estimate the distance she will move before stopping. Justify any assumptions you made.

Manish Kumar

Numerade Educator

05:39

Problem 92

Design, perform, and analyze the results of an experiment to determine the coefficient of static friction and the coefficient of kinetic friction between a penny and the cover of this textbook.

Manish Kumar

Numerade Educator

00:56

Problem 93

A sled starts at the top of the hill shown in Figure $P 4.93 .$ Add any information that you think is reasonable about the process that ensues when the sled goes down the hill and finally stops. Then tell everything you can about this process.

Manish Kumar

Numerade Educator

00:23

Problem 94

Choose the best force diagram for the pendulum bob as the plane is accelerating down the runway (Figure $P 4.94$ ).

Manish Kumar

Numerade Educator

01:49

Problem 95

The professor used which of the following expressions for the pendulum bob acceleration $(\theta$ is the angle of the pendulum bob string relative to the vertical)?
(a) $a=g \sin \theta$
(b) $a=g \cos \theta$
(c) $a=g \tan \theta$
(d) None of the choices

Manish Kumar

Numerade Educator

01:03

Problem 96

Approximately when did the peak acceleration occur?
(a) $25 \mathrm{s}$
(b) $20 \mathrm{s}$
(c) $10 \mathrm{s}$
(d) $5 \mathrm{s}$

Manish Kumar

Numerade Educator

00:47

Problem 97

Approximately when did the peak speed occur?
(a) $25 \mathrm{s}$
(b) $20 \mathrm{s}$
(c) $10 \mathrm{s}$
(d) $5 \mathrm{s}$

Manish Kumar

Numerade Educator

01:07

Problem 98

Choose the best velocity-versus-time graph below for the airplane (Figure $\mathbf{P 4 . 9 8}$ ).

Manish Kumar

Numerade Educator

00:48

Problem 99

Which answer below is closest to the magnitude of the normal force that the idealized in-run exerts on the 60 -kg skier?
(a) $590 \mathrm{N}$
(b) $540 \mathrm{N}$
(c) $250 \mathrm{N}$
(d) $230 \mathrm{N}$

Manish Kumar

Numerade Educator

01:39

Problem 100

Which numbers below are closest to the magnitudes of the kinetic friction force and the component of the gravitational force parallel to the idealized inclined in-run?
(a) $30 \mathrm{N}, 540 \mathrm{N}$
(b) $27 \mathrm{N}, 540 \mathrm{N}$
(c) $12 \mathrm{N}, 540 \mathrm{N}$
(d) $30 \mathrm{N}, 230 \mathrm{N}$
(e) $27 \mathrm{N}, 230 \mathrm{N}$
(f) $12 \mathrm{N}, 230 \mathrm{N}$

Manish Kumar

Numerade Educator

01:43

Problem 101

Which answers below are closest to the magnitude of the skier's acceleration while moving down the idealized in-run and to the skier's speed when leaving its end?
(a) $9.8 \mathrm{m} / \mathrm{s}^{2}, 48 \mathrm{m} / \mathrm{s}$
(b) $4.3 \mathrm{m} / \mathrm{s}^{2}, 32 \mathrm{m} / \mathrm{s}$
(c) $4.3 \mathrm{m} / \mathrm{s}^{2}, 28 \mathrm{m} / \mathrm{s}$
(d) $3.4 \mathrm{m} / \mathrm{s}^{2}, 32 \mathrm{m} / \mathrm{s}$
(e) $3.4 \mathrm{m} / \mathrm{s}^{2}, 28 \mathrm{m} / \mathrm{s}$

Manish Kumar

Numerade Educator

02:31

Problem 102

Assume that the skier left the ramp moving horizontally. Treat the skier as a point-like particle and assume the force exerted by air on him is minimal. If he landed 125 m diagonally from the end of the in-run, and the landing region beyond the in-run was inclined $35^{\circ}$ below the horizontal for its entire length, which answer below is closest to the time interval that he was in the air?
(a) $1.9 \mathrm{s}$
(b) $2.4 \mathrm{s}$
(c) $3.1 \mathrm{s}$
(d) $3.8 \mathrm{s}$
(e) $4.3 \mathrm{s}$

Manish Kumar

Numerade Educator

02:09

Problem 103

Using the same assumptions as stated in Problem 4.102, which answer below is closest to the jumper's speed when leaving the in-run?
(a) $37 \mathrm{m} / \mathrm{s}$
(b) $31 \mathrm{m} / \mathrm{s}$
(c) $27 \mathrm{m} / \mathrm{s}$
(d) $24 \mathrm{m} / \mathrm{s}$
(e) $21 \mathrm{m} / \mathrm{s}$

Manish Kumar

Numerade Educator

02:28

Problem 104

Which factors below would keep the skier in the air longer and contribute
to a longer jump?
1. The ramp at the end of the in-run is level instead of slightly tilted down.
2. The skier extends his body forward and positions his skis in a V shape.
3. The skier has wider and longer than usual skis.
4. The skier pushes upward off the end of the ramp at the end of the in-run.
5. The skier crouches in a streamline position when going down the in-run.
(a) 1
(b) 5
(c) 1,3,5
(d) 2,3,4
(e) 1,2,4,5
(f) 1,2,3,4,5

Manish Kumar

Numerade Educator