In Figure $\mathbf{P} 2.1$ you see unlabeled force diagrams for balls in different situations. Match the diagrams with the following descriptions. (1) A ball is moving upward after it leaves your hand. ( 2 ) You hold a ball in your hand. (3) A ball is falling down. (4) You are throwing a ball (still in your hand) straight

up. (5) You are lifting a ball at a constant pace. Explain your choices. Label the forces on the diagrams.

Zeinab A.

Numerade Educator

Draw a force diagram (a) for a bag hanging at rest from a spring; $(b)$ for the same bag sitting on a table; and $(c)$ for the same bag that you start to lift so it moves up faster and faster.

Chris M.

Numerade Educator

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 horizontally. (b) A bus moving on a horizontal road slows down in order to stop. (c) You lift your overnight bag into the overhead compartment on an airplane.

Chris M.

Numerade Educator

You hang a book bag on a spring scale and place the bag on a platform scale so that the platform scale reads 25.7 $\mathrm{N}$ and the spring scale reads 17.6 $\mathrm{N} .$ (a) Draw a force diagram to represent the situation. (b) What is the magnitude of the force that Earth exerts on the bag?

Chris M.

Numerade Educator

A block of dry ice slides at constant velocity along a smooth, horizontal surface (no friction). (a) Construct a motion dia- gram. (b) Draw position- and velocity-versus-time graphs. (c) Construct a force diagram for the block for three instances represented by dots on the motion diagram. Are the diagrams

consistent with each other?

Chris M.

Numerade Educator

You throw a ball upward. (a) Draw a motion diagram and two force diagrams for the ball on its way up and another motion diagram and two force diagrams for the ball on its way down. (b) Represent the motion of the ball with a position-versus-time graph and velocity-versus-time graph.

Chris M.

Numerade Educator

A string pulls horizontally on a cart so that it moves at increasing speed along a smooth, frictionless, horizontal surface. When the cart is moving medium-fast, the pulling is stopped abruptly. (a) Describe in words what happens to the cart's motion when the pulling stops. (b) Illustrate your description with motion diagrams, force diagrams, and position-versus-time and velocity-versus-time graphs. Indicate on the graphs when the pulling stopped. What assumptions did you make?

Chris M.

Numerade Educator

Solving the previous problem, your friend says that after the

string stops pulling, the cart starts slowing down. (a) Give a

reason for his opinion. (b) Do you agree with him? Explain

your opinion. (c) Explain how you can design an experiment

to test his idea.

Chris M.

Numerade Educator

A string pulls horizontally on a cart so that it moves at increasing speed along a smooth, frictionless, horizontal surface. When the cart is moving medium-fast, the magnitude of the pulling force is reduced to half its former magnitude. (a) Describe what happens to the cart's motion after the reduction in the string pulling. (b) Illustrate your description with motion diagrams, force diagrams, and position-versus-

time and velocity-versus-time graphs.

Chris M.

Numerade Educator

Solving the previous problem, your friend says that if the string pulls half as hard, the cart should move half as fast compared to the speed it moved when the string was pulling twice as hard. (a) Explain why your friend would think this way. (b) Do you agree with his opinion? (c) Explain how you would

convince him that he is incorrect.

Chris M.

Numerade Educator

Three motion diagrams for a moving elevator are shown in Figure $\mathbf{P} 2.11$ . Construct two force diagrams for the elevator for each motion diagram. Be sure that the lengths of the force arrows

are the appropriate relative lengths and that there is consistency between the force diagrams and the

motion diagrams. What assumptions did you make?

Chris M.

Numerade Educator

An elevator is pulled upward so it moves with increasing upward speed- the force exerted by the cable on the elevator is constant and greater than the downward gravitational force exerted by Earth. When the elevator is moving up medium-fast, the force exerted by the cable on the elevator changes abruptly to just balance the downward gravitational force of Earth - the sum of the forces that the cable and Earth exert on the elevator is now zero. Now what happens to the elevator? Explain. Represent your answer with position-versus-time and velocity-versus-time graphs. What assumptions did you make?

Chris M.

Numerade Educator

Solving the previous problem, your friend says that the

elevator will stop if the two forces have equal magnitudes.

(a) Why would he think this way? (b) Do you agree with his

opinion? (c) If you disagree, how would you convince him

that he is incorrect?

Chris M.

Numerade Educator

A block of dry ice slides at a constant velocity on a smooth,

horizontal, frictionless surface. A second block of dry ice

slides twice as fast on the same surface (at a higher constant

velocity). Compare the resultant forces exerted on each block.

Explain your reasoning.

Chris M.

Numerade Educator

An elevator moves downward at constant velocity. Construct

a motion diagram and three consecutive force diagrams for

the elevator (ignore the resistive force exerted by the air on

the elevator) as it is moving. Make the relative lengths of the

force arrows consistent with the motion diagram.

Chris M.

Numerade Educator

Figures $\mathrm{P} 2.11 \mathrm{a}, \mathrm{b}$ , and $\mathrm{c}$ show three motion diagrams for an elevator moving downward. (a) For each diagram, say everything you can about the elevator's motion. (b) Draw a force diagram for each motion diagram. (c) Could you draw a different motion diagram for each force diagram? Explain how it is possible.

Chris M.

Numerade Educator

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?

Chris M.

Numerade Educator

A train traveling from New York to Philadelphia is passing a station. A ball is sitting on the floor of the train not moving with respect to the train. (a) Draw a force diagram and a motion diagram for the ball as seen by the observers on the train and on the platform. (b) The ball now starts accelerating forward relative to the floor. Draw force and motion diagrams for the ball as seen by the observers on the train and on the platform. Which of the observers can use Newton's first law to explain the ball's acceleration? Explain.

Chris M.

Numerade Educator

Explain the phenomenon of whiplash from two points of

view: that of an observer on the ground and an observer in

the car.

Chris M.

Numerade Educator

An astronaut exerts a $100-\mathrm{N}$ force pushing a beam into place

on the International Space Station. The beam accelerates at

0.10 $\mathrm{m} / \mathrm{s}^{2} .$ Determine the mass of the beam. What is the percent uncertainty in your answer?

Chris M.

Numerade Educator

Four people participate in a rope competition. Two of them

pull the rope right, exerting forces of magnitude 330 $\mathrm{N}$ and

380 $\mathrm{N}$ . The other two pull left, exerting forces of magnitude

300 $\mathrm{N}$ and 400 $\mathrm{N}$ . What is the sum of the forces exerted on a

short section in the middle of the rope?

Chris M.

Numerade Educator

Shot put throw During a practice shot put throw, the 7.0 -kg shot left world champion $\mathrm{C}$ . J. Hunter's hand at speed 13 $\mathrm{m} / \mathrm{s}$ . While making the throw, his hand pushed the shot a distance of 1.7 $\mathrm{m}$ . Describe all the physical quantities you can determine using this information. Describe the assumptions you need to make to determine them.

Chris M.

Numerade Educator

You know the sum of the forces $\sum \vec{F}$ exerted on an object of mass $m$ during $\Delta t$ seconds. The object is at rest at the beginning of the time interval. List three physical quantities

that you can determine about that object's motion using this information. Then explain how you will determine them.

Chris M.

Numerade Educator

You record the displacement of an object as a constant force is exerted on it. (a) If the time interval during which the force is exerted doubles, how does the object's displacement change? Indicate all the assumptions that you made. (b) Explain how your answer changes if one of the assumptions is not valid.

Chris M.

Numerade Educator

" Equation Jeopardy 1 Invent a problem for which the following equation can be a solution:

$$200 \mathrm{N}-40 \mathrm{N}=(40 \mathrm{kg}) a_{x}$$

Chris M.

Numerade Educator

Equation Jeopardy 2 Describe in words a problem for which the following equation is a solution and draw a force diagram that is consistent with the equation (specify the direction of the axis):

$$+29.4 \mathrm{N}-F_{\mathrm{R} \text { on } \mathrm{O}}=(3.0 \mathrm{kg})\left(3.0 \mathrm{m} / \mathrm{s}^{2}\right)$$

Tiannie Z.

Numerade Educator

Equation Jeopardy 3 Describe in words a problem for which the following equation is a solution and draw a force diagram that is consistent with the equation (specify the direction of the axis):

$$100 \mathrm{N}-f_{\mathrm{SonO}}=(30 \mathrm{kg})\left(-1.0 \mathrm{m} / \mathrm{s}^{2}\right)$$

Tiannie Z.

Numerade Educator

Equation Jeopardy 4 Describe in words a problem for which the following equation is a solution and draw a force diagram that is consistent with the equation (specify the direction of the axis):

$$-196 \mathrm{N}+F_{\mathrm{P} \text { on } \mathrm{O}}=(20 \mathrm{kg})\left(-2.0 \mathrm{m} / \mathrm{s}^{2}\right)$$

Tiannie Z.

Numerade Educator

Spider-Man Spider-Man holds the bottom of an elevator with one hand. With his other hand, he holds a spider cord attached to a $50-\mathrm{kg}$ box of explosives at the bottom of the

cord. Determine the force that the cord exerts on the box if (a) the elevator is at rest; (b) the elevator accelerates up at $2.0 \mathrm{m} / \mathrm{s}^{2} ;(\mathrm{c})$ the upward-moving elevator's speed decreases at a rate of $2.0 \mathrm{m} / \mathrm{s}^{2} ;$ and ( $\mathrm{d}$ ) the elevator falls freely.

Tiannie Z.

Numerade Educator

A farmer pushes his 500 -kg wagon along a horizontal level icy road, exerting a $125-\mathrm{N}$ horizontal force on the wagon. (a) Determine the acceleration of the wagon. How certain are

you about your answer? What assumptions did you make? Would the number be higher or lower if you did not make those assumptions? (b) If the wagon started at rest, how fast was it moving after being pushed for 5.0 $\mathrm{s} ?$

Kevin S.

Numerade Educator

Stuntwoman The downward acceleration of a 60 -kg stunt- woman near the end of a fall from a very high building is 7.0 $\mathrm{m} / \mathrm{s}^{2} .$ What resistive force does the air exert on her body

at that point?

Tiannie Z.

Numerade Educator

Estimate the average force that a baseball pitcher's hand

exerts on a 0.145 -kg baseball as he throws a 40 $\mathrm{m} / \mathrm{s}(90 \mathrm{mi} / \mathrm{h})$

pitch. Indicate all of the assumptions you made.

Mayukh B.

Numerade Educator

Super Hornet jet takeoff A $2.1 \times 10^{4}-\mathrm{kg} \mathrm{F}-18$ Super Hornet jet airplane (see Figure $\mathrm{P} 2.33 )$ goes from zero to 265 $\mathrm{km} / \mathrm{h}$ in 90 $\mathrm{m}$ during takeoff from the flight deck of the USS Nimitz aircraft carrier. What physical quantities can you determine using this information? Make a list and determine the values of three of them.

Kevin S.

Numerade Educator

Lunar Lander The Lunar Lander of mass $2.0 \times 10^{4} \mathrm{kg}$

made the last 150 $\mathrm{m}$ of its trip to the Moon's surface in 120 $\mathrm{s}$

descending at approximately constant speed. The Handbook

of Lunar Pilots indicates that the gravitational constant on the

Moon is 1.633 $\mathrm{N} / \mathrm{kg}$ . Using these quantities, what can you

learn about the Lunar Lander's motion?

Kevin S.

Numerade Educator

A Navy Seal of mass 80 kg parachuted into an enemy harbor. At one point while he was falling, the resistive force of air exerted on him was 520 $\mathrm{N}$ . What can you determine about his

motion?

Tiannie Z.

Numerade Educator

Astronaut Karen Nyberg, a 60 -kg astronaut, sits on a bathroom scale in a rocket that is taking off vertically with an acceleration of 3$g .$ What does the scale read?

Jacob T.

Numerade Educator

A 0.10 -kg apple falls off a tree branch that is 2.0 $\mathrm{m}$ above the grass. The apple sinks 0.060 $\mathrm{m}$ into the grass while stopping. Determine the force that the grass exerts on the apple

while stopping it. Indicate any assumptions you made.

Kevin S.

Numerade Educator

An 80 -kg fireman slides 5.0 $\mathrm{m}$ down a fire pole. He holds the pole, which exerts a $500-\mathrm{N}$ steady resistive force on the fireman. At the bottom he slows to a stop in 0.40 $\mathrm{m}$ by bending his knees. What can you determine using this information? Determine it.

Kevin S.

Numerade Educator

Earth exerts a $1.0-\mathrm{N}$ gravitational force on an apple as it falls

toward the ground. (a) What force does the apple exert on Earth? (b) Compare the accelerations of the apple and Earth due to these forces. The mass of the apple is about 100 $\mathrm{g}$ and

the mass of Earth is about $6 \times 10^{24} \mathrm{kg} .$

Kevin S.

Numerade Educator

You push a bowling ball down the lane toward the pins. Draw force diagrams for the ball (a) just before you let it go; (b) when the ball is rolling (for two clock readings); (c) as the ball is hitting a bowling pin. (d) For each force exerted on the ball in parts (a)-(c), draw the Newton's third law force beside the force diagram, and indicate the object on which these third law forces are exerted.

Kevin S.

Numerade Educator

(a) A 50 -kg skater initially at rest throws a 4 -kg medicine ball horizontally. Describe what happens to the skater and to the ball. (b) Estimate the acceleration of the ball during the throw and of the skater using a reasonable value for the force that a skater can exert on the medicine ball. (c) The skater

moving to the right catches the ball moving to the left. After the catch, both objects move to the right. Draw force diagrams for the skater and for the ball while the ball is being caught.

Mayukh B.

Numerade Educator

Basketball player LeBron James can jump vertically over 0.9 $\mathrm{m}$ . Estimate the force that he exerts on the surface of the basketball court as he jumps. (a) Compare this force with the force that the surface exerts on James. Describe all assumptions used in your estimate and state how each assumption affects the result. (b) Repeat the problem looking at the time interval when he is landing back on the floor.

Mayukh B.

Numerade Educator

The Scottish Tug of War Association contests involve eight-person teams pulling on a rope in opposite directions. Estimate the force that the rope exerts on each team. Indicate any assumptions you made and include a force diagram for a short section of the rope.

Mayukh B.

Numerade Educator

A bowling ball hits a pin. (a) Draw a force diagram and a motion diagram for the ball during the collision and separate diagrams for the pin. (b) Explain why your friend who has not taken physics would insist that the bowling ball hits the pin harder than the pin hits the ball.

Mayukh B.

Numerade Educator

Car safety The National Transportation Safety Bureau indicates that a person in a car crash has a reasonable chance of survival if his or her acceleration is less than 300 $\mathrm{m} / \mathrm{s}^{2}$

(a) What magnitude force would cause this acceleration in such a collision? (b) What stopping distance is needed if the initial speed before the collision is 20 $\mathrm{m} / \mathrm{s}(72 \mathrm{km} / \mathrm{h} \text { or }$ 45 $\mathrm{mi} / \mathrm{h}$ )? (c) Indicate any assumptions you made.

Mayukh B.

Numerade Educator

A 70 -kg person in a moving car stops during a car collision in a distance of 0.60 $\mathrm{m}$ . The stopping force that the air bag exerts on the person is 8000 $\mathrm{N}$ . Name at least three physical

quantities describing the person's motion that you can determine using this information, and then determine them.

Mayukh B.

Numerade Educator

Left ventricle pumping The lower left chamber of the heart (the left ventricle) pumps blood into the aorta. According to biophysical studies, a left ventricular contraction lasts about 0.20 s and pumps 88 $\mathrm{g}$ of blood. This blood starts at rest and after 0.20 $\mathrm{s}$ is moving through the aorta at about 2 $\mathrm{m} / \mathrm{s}$ . (a) Estimate the force exerted on the blood by the left

ventricle. $(\mathrm{b})$ What is the percent uncertainty in your answer? (c) What assumptions did you make? Did the assumptions increase or decrease the calculated value of the force compared to the actual value?

Mayukh B.

Numerade Educator

Acorn hits deck You are sitting on a deck of your house surrounded by oak trees. You hear the sound of an acorn hitting the deck. You wonder if an acorn will do much damage if instead of the deck it hits your head. Make appropriate estimations and assumptions and provide a reasonable answer.

Mayukh B.

Numerade Educator

Olympic dive During a practice dive, Olympic diver Fu Mingxia reached a maximum height of 5.0 $\mathrm{m}$ above the water. She came to rest 0.40 $\mathrm{s}$ after hitting the water. Estimate

the average force that the water exerted on her while stopping her.

Mayukh B.

Numerade Educator

The brakes on a bus fail as it approaches a turn. The bus is traveling at the speed limit before it moves about 23 $\mathrm{m}$ across grass before hitting a wall. A bicycle on the bike rack on the front of the bus is crushed, but there is little damage to the bus. (a) Draw force diagrams for the bus and the wall

during the collision. (b) Estimate the average force that the bicycle and bus exert on the wall while stopping. Indicate any assumptions made in your estimate.

Mayukh B.

Numerade Educator

You are doing squats on a bathroom scale. You decide to push off the scale and jump up. Estimate the reading as you push off and as you land. Indicate any assumptions you made.

Mayukh B.

Numerade Educator

Estimate the horizontal speed of the runner shown in Figure $\mathbf{P} 2.52$ at the instant she leaves contact with the starting blocks. Indicate any assumptions you made.

Mayukh B.

Numerade Educator

Estimate the maximum acceleration of Earth if all people got together and jumped up simultaneously.

Mayukh B.

Numerade Educator

Estimate how much Earth would move during the jump described in Problem 53 .

Mayukh B.

Numerade Educator

In an early practice run while the rocket sled was stopping, a passenger dummy broke its restraining device and the window of the rocket sled and stopped after skidding down the track. What physics principle best explains this outcome?

\begin{equation}\begin{array}{ll}{\text { (a) Newton's first law }} & {\text { (b) Newton's second law }} \\ {\text { (c) Newton's third law }} & {\text { (d) The first and second }} \\ {\text { laws }} \\ {\text { (e) All three laws }}\end{array}\end{equation}

Mayukh B.

Numerade Educator

Which answer below is closest to Stapp's 67 $\mathrm{m} / \mathrm{s}$ speed in

miles per hour?

$\begin{array}{llll}{\text { (a) } 30 \mathrm{mi} / \mathrm{h}} {\text { (b) } 40 \mathrm{mi} / \mathrm{h}} & {\text { (c) } 100 \mathrm{mi} / \mathrm{h}} \\ (d) 120 \mathrm{mi} / \mathrm{h} \quad \text { (e) } 150 \mathrm{mi} / \mathrm{h}\end{array}$

Mayukh B.

Numerade Educator

Which answer below is closest to the magnitude of the acceleration of Stapp and his sled as their speed increased from zero to 67 $\mathrm{m} / \mathrm{s}$ ?

\begin{equation}\begin{array}{ll}{\text { (a) } 5 \mathrm{m} / \mathrm{s}^{2}} & {\text { (b) } 6 \mathrm{m} / \mathrm{s}^{2}} & {\text { (c) } 10 \mathrm{m} / \mathrm{s}^{2}} \\ {\text { (d) } 12 \mathrm{m} / \mathrm{s}^{2}} & {\text { (e) } 14 \mathrm{m} / \mathrm{s}^{2}}\end{array}\end{equation}

Mayukh B.

Numerade Educator

Which answer below is closest to the magnitude of the acceleration of Stapp and his sled as their speed decreased from 67 m>s to zero?

(a) 12 g (b) 19 g (c) 26 g

(d) 38 g (e) 48 g

Mayukh B.

Numerade Educator

Which answer below is closest to the average force exerted by the restraining system on 80-kg Stapp while his speed decreased from 67 m/s to zero in a distance of 6.0 m?

(a) 10,000 N (b) 20,000 N (c) 30,000 N

(d) 40,000 N (e) 50,000 N

Mayukh B.

Numerade Educator

Which answer below is closest to the time interval for Stapp and his sled to stop as their speed decreased from 67 m/s to zero?

(a) 0.09 s (b) 0.18 s (c) 0.34 s

(d) 5.4 s (e) 10.8 s

Mayukh B.

Numerade Educator

The downward distance $d$ that an object falls in a time interval $t$

if starting at rest is $d=\frac{1}{2} a t^{2}$ . On the Moon, a rock falls 10.0 $\mathrm{m}$

in 3.50 s. How far will the object fall in 5.00 $\mathrm{s}$ , assuming the

same acceleration?

(a) 14.3 m (b) 20.4 m (c) 4.90 m

(d) 7.00 m (e) 10.0 m

Mayukh B.

Numerade Educator

The downward distance $d$ that an object falls in a time interval $t$

if starting at rest is $d=\frac{1}{2} a t^{2}$ . On the Moon, a rock falls 10.0 $\mathrm{m}$

in 3.50 s. What time interval $t$ is needed for it to fall $15.0 \mathrm{m},$

assuming the same acceleration?

(a) 2.33 s (b) 2.86 s (c) 3.50 s

(d) 4.29 s (e) 5.25 s

Mayukh B.

Numerade Educator

A car’s braking distance d (the distance it travels if rolling to a stop after the brakes are applied) depends on its initial speed $v_{0},$ the maximum friction force $\vec{f}_{\mathrm{R} \text { on } \mathrm{C}}$ exerted by the road on the car, and the car's mass $m$ according to the equation

$$\frac{2 f_{s \max }}{m} d=v_{0}^{2}$$

Suppose the braking distance for a particular car and road surface is 26 $\mathrm{m}$ when the initial speed is 18 $\mathrm{m} / \mathrm{s} .$ What is the braking distance when traveling at 27 $\mathrm{m} / \mathrm{s} ?$

(a) 59 m (b) 39 m (c) 26 m

(d) 17 m (e) 12 m

Mayukh B.

Numerade Educator

You decide to open a pizza parlor. The ingredients require that you charge $\$ 4.50$ for a 7.0 -in. -diameter pizza. How large should you make a pizza whose price is $\$ 10.00$ , assuming the

cost is based entirely on the cost of ingredients?

(a) 1.4 in. (b) 3.1 in. (c) 7.0 in.

(d) 10 in. (e) 16 in.

Mayukh B.

Numerade Educator

A circular wool quilt of 1.2 $\mathrm{m}$ diameter costs $\$ 200 .$ What

should the price of a $1.6-\mathrm{m}$ -diameter quilt be if it is to have

the same cost per unit area?

$\begin{array}{lllll}{\text { (a) } \$ 110} & {\text { (b) } \$ 150} & {\text { (c) } \$ 270} & {\text { (d) } \$ 360}\end{array}$

Mayukh B.

Numerade Educator