College Physics 2013

Determine the $x$ . and $y$ -components of each force vector shown in Figure P3.1.

Determine the $x$ - and $y$ -components of each force vector shown in Figure P3.2.

Determine the $x$ - and $y$ -components of each displacement shown in Figure $P 3.3$ .

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 $(\mathrm{c})(-400 \mathrm{N},+300 \mathrm{N})$

The x- and y -scalar components of several unknown forces are listed below 1Fx , Fy2. 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) 1-200 N, +100 N2, (b) 1+300 N, +400 N2, and (c) 1+400 N, -300 N2.

Three ropes pull on a knot shown in Figure P3.6a. The knot is not accelerating. A partially completed force diagram for the knot is shown in Figure P 3.6 $\mathrm{b}$ . Use qualitative reasoning (no math) to determine the magnitudes of the forces that ropes 2 and 3 exert on the knot. Explain in words how you arrived at your answers.

Solve the previous problem quantitatively using Newton's second law.

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 above the horizontal. (b) A bus moving on a horizontal road slows in order to stop. (c) You slide down an inclined water slide. (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 horizon- tally on a second rope attached to the right side of the right box (consider each box separately).

"Write Newton's second law in component form for each of the situations described in Problem 8 .

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 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).

" Write Newton's second law in component form for each of the situations described in Problem 10.

Apply Newton’s second law in component form for the force diagram shown in Figure P3.1.

" Apply Newton's second law in component form for the force diagram shown in Figure $\mathrm{P} 3.2$ .

Equation Jeopardy 1 The equations below are the horizontal x - and vertical y - component forms of Newton’s second law applied to a physical process. 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 might be an answer (there are many possibilities).
$$
\begin{aligned}(5.0 \mathrm{kg}) a_{x}=&(30 \mathrm{N}) \cos 30^{\circ}+N \cos 90^{\circ} \\ &-(5.0 \mathrm{kg})(9.8 \mathrm{N} / \mathrm{kg}) \cos 60^{\circ} \\(5.0 \mathrm{kg}) 0=&(30 \mathrm{N}) \sin 30^{\circ}+\mathrm{N} \sin 90^{\circ} \\ &-(5.0 \mathrm{kg})(9.8 \mathrm{N} / \mathrm{kg}) \sin 60^{\circ} \end{aligned}
$$

Equation Jeopardy 2 The equations below are the horizontal $x$ - and vertical $y$ -component forms of Newton's second law applied to a physical process for an object on an incline. Solve for the unknowns. Then work backward and construct a force diagram for the object and invent a problem for which the
equations might be an answer (there are many possibilities).
$$
\begin{aligned}(5.0 \mathrm{kg}) a_{x}=&(30 \mathrm{N}) \cos 30^{\circ}+N \cos 90^{\circ} \\ &-(5.0 \mathrm{kg})(9.8 \mathrm{N} / \mathrm{kg}) \cos 60^{\circ} \\(5.0 \mathrm{kg}) 0=&(30 \mathrm{N}) \sin 30^{\circ}+N \sin 90^{\circ} \\ &-(5.0 \mathrm{kg})(9.8 \mathrm{N} / \mathrm{kg}) \sin 60^{\circ} \end{aligned}
$$

Equation Jeopardy 3 The equations below are the horizontal x- and vertical y-component forms of Newton’s second law and a kinematics equation applied to a physical process. 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 might be an answer (there are many possibilities). Provide all the information you know about your process.
$$
\begin{aligned}(5.0 \mathrm{kg}) a_{x}=&(50 \mathrm{N}) \cos 30^{\circ}+N \cos 90^{\circ} \\ &+(5.0 \mathrm{kg})(9.8 \mathrm{N} / \mathrm{kg}) \cos 90^{\circ} \end{aligned}
$$
$$
\begin{aligned}(5.0 \mathrm{kg}) 0=&(-50 \mathrm{N}) \sin 30^{\circ}+N \sin 90^{\circ} \\ &-(5.0 \mathrm{kg})(9.8 \mathrm{N} / \mathrm{kg}) \sin 90^{\circ} \end{aligned}
$$
$$
x-0=(2.0 \mathrm{m} / \mathrm{s})(4.0 \mathrm{s})+\frac{1}{2} a_{x}(4.0 \mathrm{s})^{2}
$$

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 for 10 $\mathrm{m}$ . List all the quantities you can determine using these givens and determine three of the quantities on the list.

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 u 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.

Olympic 100 -m dash start At the start of his race, $86-\mathrm{kg}$ Olympic 100 -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.

Accelerometer A string with one 10 -g washer on the end is attached to the rearview mirror of a car. When the car leaves an intersection, the string makes an angle of $5^{\circ}$ with the vertical. What is the acceleration of the car? [Hint: Choose the washer as the system object for your force diagram. Use the vertical component equation of Newton's second law to find the magnitude of the force that the string exerts on the washer. Then continue with the horizontal component equation. $.$

Your own accelerometer A train has an accleration 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 every. thing you can about the pendulum during the deceleration of the train.

Skier A 52 -kg skier starts at rest and slides 30 $\mathrm{m}$ 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).

Ski rope tow 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 -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.

Soapbox racecar 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?

Whiplash experience 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 $\mathrm{P} 3.25$ about 300 $\mathrm{m} / \mathrm{s}^{2}$ . Figure $\mathrm{P} 3.25$ shows an arrow that represents the force that the neck muscle exerts on the head so that it ac-celerates forward with the body instead of flipping backward. If the head has a mass of $4.5 \mathrm{kg},$ 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 $\vec{F} ?$

Iditarod race practice The dogs of four-time Iditarod Trail Sled Dog Race champion Jeff King pull two 100-kg sleds that are connected by a rope. The sleds move on an icy surface. The dogs exert a 240-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.

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 $\mathrm{m} / \mathrm{s}^{2}$ .

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.

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?

"Repeat Problem $29,$ only this time with the sleds on a hill.

Your daredevil friends attach a rope to a 140 -kg sled that rests on a frictionless icy surface. The rope extends horizontally to a smooth dead tree trunk lying at the edge of a cliff. Another person attaches a 30 -kg rock at the end of the rope after it passes over the tree trunk and then releases the rock-
the rope is initially taut. Determine the acceleration of the sled, the force that the rope exerts on the sled and on the rock, and the time interval during which the person can jump off the sled before it reaches the cliff 10 $\mathrm{m}$ ahead. There is no friction between the rope and the tree trunk.

Assume the scenario described in Problem $31,$ but in this case a hanging rock of unknown mass accelerates downward at 2.7 $\mathrm{m} / \mathrm{s}^{2}$ and pulls the sled with it. Determine the mass of the hanging rock and the force that the rope exerts on the sled. There is no friction between the rope and the tree trunk.

The $20-\mathrm{kg}$ block shown in Figure $P 3.33$ accelerates down and to the left, and the $10-\mathrm{kg}$ block accelerates up. Find the magnitude of this acceleration and the force that the cable ex-erts on a block. There is no friction between the block and the- inclined plane, and the pulley is
frictionless and light.

A person holds a $200-g$ block that is connected to a $250-g$ block by a string going over a light pulley with no friction in the bearing (an Atwood machine). After the person releases the 200 -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 $\mathrm{m} ?$

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?

Equation Jeopardy 4 The equations below are the horizontal $x$ - and vertical $y$ -component forms of Newton's second law applied to a physical process. 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 might provide an answer (there are many possibilities).
$$
\begin{aligned}(5.0 \mathrm{kg}) a_{x}=&(50 \mathrm{N}) \cos 30^{\circ}+N \cos 90^{\circ}-0.5 N \cos 0^{\circ} \\ &+(5.0 \mathrm{kg})(9.8 \mathrm{N} / \mathrm{kg}) \cos 90^{\circ} \\(5.0 \mathrm{kg}) 0=&(-50 \mathrm{N}) \sin 30^{\circ}+N \sin 90^{\circ}+0.5 N \sin 0^{\circ} \\ &-(5.0 \mathrm{kg})(9.8 \mathrm{N} / \mathrm{kg}) \sin 90^{\circ} \end{aligned}
$$

Equation Jeopardy 5 The equations below are the $x$ -and $y$ -component forms of Newton's second law applied to a physical process for an object on an incline. Solve for the unknowns. Then work backward and construct a force diagram for the object and invent a problem for which the equations
might provide an answer (there are many possibilities).
$$
\begin{aligned}(5.0 \mathrm{kg}) 0=&+F \cos 0^{\circ}+N \cos 90^{\circ}-0.50 N \cos 0^{\circ} \\ &-(5.0 \mathrm{kg})(9.8 \mathrm{N} / \mathrm{kg}) \cos 60^{\circ} \\(5.0 \mathrm{kg}) 0=&+F \sin 0^{\circ}+N \sin 90^{\circ}-0.50 \mathrm{N} \sin 0^{\circ} \\ &-(5.0 \mathrm{kg})(9.8 \mathrm{N} / \mathrm{kg}) \sin 60^{\circ} \end{aligned}
$$

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?

A 60 -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.

Racer runs out of gas James Stewart, 2002 Motocross $/$ Supercross Rookic of the Year, is leading a race when he runs out of gas near the finish line. He is moving at 16 $\mathrm{m} / \mathrm{s}$
when he enters a section of the course covered with sand where the effective cocfficient of friction is $0.90 .$ Will he be able to coast through this $15-\mathrm{m}$ -long section to the finish line at the end? If yes, what is his speed at the finish line?

Car stopping distance and friction A certain 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. Is this kinetic or static friction? Explain.

A 50 -kg box rests on the floor. The coefficients of static and kinetic triction 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?

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.

A wagon is accelerating to the right. A book is pressed against the back vertical side of the wagon and does not slide down. Explain how this can be.

In Problem 44, the coefficient of static friction between the book and the vertical back of the wagon is ms. Determine an expression for the minimum acceleration of the wagon in terms of ms so that the book does not slide down. Does the mass of the book matter? Explain.

A car has a mass of 1520 $\mathrm{kg}$ . 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.

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.

You want to use a rope to pull a 10 -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.

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

Olympic skier Olympic skier Lindsey Vonn 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 Vonn's acceleration, and her speed 6.0 s after starting.

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

A crate of mass m sitting on a horizontal floor is attached to a rope that pulls at an angle u above the horizontal. The coefficient of static friction between the crate and floor is ms. (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.

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

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

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 non-
zero speed while sliding.

Equation Jeopardy 6 The cquations below describe a projectile's path. Solve for the unknowns and then invent a process that the equations might describe. There are many possibilities.
$$
\begin{array}{l}{x=0+(20 \mathrm{m} / \mathrm{s})\left(\cos 0^{\circ}\right) t} \\ {0=8.0 \mathrm{m}+(20 \mathrm{m} / \mathrm{s})\left(\sin 0^{\circ}\right)-\frac{1}{2}\left(9.8 \mathrm{m} / \mathrm{s}^{2}\right) t^{2}}\end{array}
$$

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.

A ball moves in an arc through the air (see Figure P3.5 8 ). Construct a force diagram for the ball when at positions ( a), and (c). Ignore the resistive force exerted by the air on the ball.

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.

A baseball leaves a bat and flies upward and toward center field. After it leaves the bat, are any forces exerted on the ball in the horizontal direction? In the direction of motion? In the vertical direction? If so, identify the other object that causes each force. Do not ignore air resistance.

Robbie Knievel ride 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.

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 speed must she be launched to cross the 520 -m gap?

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 the ball be kicked? Assume that the ball leaves 1.0 $\mathrm{m}$ above the ground.

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?

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.

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.

When you actually perform the experiment described in Problem $66,$ 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.

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 if you aim $30^{\circ}$ above the horizontal? (c) Deter-
mine the maximum distance that you can move the target and hit it with the arrow.

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 $\mathrm{m} / \mathrm{s}$ .

Three force diagrams for a car are shown in Figure P3.70. Indicate as many situations as possible for the car in terms of its velocity and acceleration at that instant for each diagram.

"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 $\mathrm{N}$ . Determine the magnitude of the force that causes the minivan to accelerate in the forward direction.

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

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

Two blocks of masses $m_{1}$ and $m_{2}$ hang at the ends of string that passes over the very light pulley with low friction bearings shown in Figure P3.74. 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?

A 0.20 -kg block placed on an inclined plane (angle $30^{\circ}$ above the horizontal) is connected by a string going over a pulley to a 0.60 -kg hanging block. Determine the acceleration of the system if there is no friction between the block and the surface of the inclined plane.

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.

A 3.5-kg object placed on an inclined plane (angle 30 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.

An object of mass m1 placed on an inclined plane (angle u above the horizontal) is connected by a string going over a pulley to a hanging object of mass m2. Determine the accelertion of the system if there is no friction between object 1 and the surface of the inclined plane. If the problem has multiple answers, explore all of them.

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 $\mu_{s},$ and the coefficient of kinetic friction is $\mu_{\mathrm{k}}$ . If the problem has multiple answers, explore all of them.

You are driving at a rea-sonable constant velocity in a van with a windshield tilted $120^{\circ}$ relative to the horizontal (see Figure $P 3.80 )$ . 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?

A ledge on a building is 20 $\mathrm{m}$ above the ground. A taut ope attached to a $4.0-\mathrm{kg}$ can of paint sitting on the ledge passes up over a pulley and straight down to a $3.0-\mathrm{kg}$ 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 floor?

Bicycle ruined The brakes on a bus fail as it approaches a turn. The bus was traveling at the speed limit be-fore it moved about 24 $\mathrm{m}$ across grass and hit a brick wall. A bicycle attached to a rack on the front of the bus was crushed between the bus and the brick wall. There was little damage
to the bus. Estimate the average force that the bicycle and bus exert on the wall while stopping. Indicate any assumptions made in your cstimate.

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.

The mass of a spacecraft is about 480 $\mathrm{kg}$ . 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 thecngine cause the craft's speed to change in 1 week of running at maximum power? Describe any assumptions you made.

A 60-kg rollerblader rolls 10 m down a 30 incline When she reaches the level floor at the bottom, she ap-
plies the brakes. Use Newton’s second law to estimate the distance she will move before stopping. Justify any assumptions you made.

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.

Tell all A sled starts at the top of the hill shown in Figure P3.87. 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.

Choose the best force diagram for the pendulum bob as the plane is accelerating down the runway (Figure P3.8.

The professor used which of the following expression for the pendulum bob acceleration $(\theta \text { is the angle of the pendulum }$ bob string relative to the vertical)?
$\begin{array}{ll}{\text { (a) } a=g \sin \theta} & {\text { (b) } a=g \cos \theta} \\ {\text { (c) } a=g \tan \theta} & {\text { (d) None of the choices }}\end{array}$

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

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

Choose the best velocity-versus-time graph below for the air- plane (Figure P3.92).

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

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?
$$
\begin{array}{ll}{\text { (a) } 30 \mathrm{N}, 540 \mathrm{N}} & {\text { (b) } 27 \mathrm{N}, 540 \mathrm{N}} \\ {\text { (d) } 30 \mathrm{N}, 230 \mathrm{N}} & {\text { (e) } 27 \mathrm{N}, 230 \mathrm{N}}\end{array}
\begin{array}{l}{\text { (c) } 12 \mathrm{N}, 540 \mathrm{N}} \\ {\text { (f) } 12 \mathrm{N}, 230 \mathrm{N}}\end{array}
$$

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

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 $\mathrm{m}$ diagonally from the end of the in-run and the landing region beyond the in-run was inclined $35^{0}$ below the horizontal for its entire length, which answer below is closest to the time interval that he was in the air?
$$
\begin{array}{ll}{\text { (a) } 1.9 \mathrm{s}} & {\text { (b) } 2.4 \mathrm{s}} \\ {\text { (d) } 3.8 \mathrm{s}} & {\text { (c) } 4.3 \mathrm{s}}\end{array}
$$

Using the same assumptions as stated in Problem $96,$ which answer below is closest to the jumper's speed when leaving the in-run?
$$
\begin{array}{ll}{\text { (a) } 37 \mathrm{m/s}} & {\text { (b) } 31 \mathrm{m} / \mathrm{s}} \\ {\text { (d) } 24 \mathrm{m} / \mathrm{s}} & {\text { (e) } 21 \mathrm{m} / \mathrm{s}}\end{array}
$$

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 slightlytilted down.
2. The skier extends his body forward and positions his skisin 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. of the in-run.
5. The skier crouches in a streamline position when going down the in-run.
$$
\begin{array}{ll}{\text { (a) } 1} & {\text { (b) } 5} \\ {\text { (d) } 2,3,4} & {\text { (e) } 1,2,4,5}\end{array}
\begin{array}{l}{\text { (c) } 1,3,5} \\ {\text { (f) } 1,2,3,4,5}\end{array}
$$