# Chapter 4

Chapter thumbnail # Chapter 4 : Dynamics: Force and Newton's Laws of Motion - all with Video Solutions

### Problem 2

A 63.0 kg sprinter accelerates at a rate of $4.20 \textrm{ m/s}^2$ for 20 m, and then maintains that velocity for the remainder of the 100-m dash, what will be his time for the race?

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### Problem 4

Since astronauts in orbit are apparently weightless, a clever method of measuring their masses is needed to monitor their mass gains or losses to adjust diets. One way to do this is to exert a known force on an astronaut and measure the acceleration produced. Suppose a net external force of 50.0 N is exerted and the astronaut’s acceleration is measured to be$0.893\textrm{ m/s}^2$ . (a) Calculate her mass. (b) By exerting a force on the astronaut, the vehicle in which they orbit experiences an equal and opposite force. Discuss how this would affect the measurement of the astronaut’s acceleration. Propose a method in which recoil of the vehicle is avoided.

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### Problem 5

In Figure 4.7, the net external force on the 24-kg mower is stated to be 51 N. If the force of friction opposing the motion is 24 N, what force (in newtons) is the person exerting on the mower? Suppose the mower is moving at 1.5 m/s when the force is removed. How far will the mower go before stopping?

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### Problem 6

The same rocket sled drawn in Figure 4.31 is decelerated at a rate of $196 \textrm{ m/s}^2$. What force is necessary to produce this deceleration? Assume that the rockets are off. The mass of the system is 2100 kg.

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### Problem 7

(a) If the rocket sled shown in Figure 4.32 starts with only one rocket burning, what is the magnitude of its acceleration? Assume that the mass of the system is 2100 kg, the thrust T is $2.4 \times 10^4 \textrm{ N}$, and the force of friction opposing the motion is known to be 650 N. (b) Why is the acceleration not one- fourth of what it is with all rockets burning?

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### Problem 8

What is the deceleration of the rocket sled if it comes to rest in 1.1 s from a speed of 1000 km/h? (Such deceleration caused one test subject to black out and have temporary blindness.)

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### Problem 9

Suppose two children push horizontally, but in exactly opposite directions, on a third child in a wagon. The first child exerts a force of 75.0 N, the second a force of 90.0 N, friction is 12.0 N, and the mass of the third child plus wagon is 23.0 kg. (a) What is the system of interest if the acceleration of the child in the wagon is to be calculated? (b) Draw a free-body diagram, including all forces acting on the system. (c) Calculate the acceleration. (d) What would the acceleration be if friction were 15.0 N?

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### Problem 10

A powerful motorcycle can produce an acceleration of $3.50\textrm{ m/s}^2$ while traveling at 90.0 km/h. At that speed the forces resisting motion, including friction and air resistance, total 400 N. (Air resistance is analogous to air friction. It always opposes the motion of an object.) What is the magnitude of the force the motorcycle exerts backward on the ground to produce its acceleration if the mass of the motorcycle with rider is 245 kg?

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### Problem 11

The rocket sled shown in Figure 4.33 accelerates at a rate of $49.0 \textrm{ m/s}^2$. Its passenger has a mass of 75.0 kg. (a) Calculate the horizontal component of the force the seat exerts against his body. Compare this with his weight by using a ratio. (b) Calculate the direction and magnitude of the total force the seat exerts against his body.

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### Problem 12

The rocket sled shown in Figure 4.33 decelerates at a rate of $201 \textrm{ m/s}^2$. Its passenger has a mass of 75.0 kg. (a) Calculate the horizontal component of the force the seat exerts against his body. Compare this with his weight by using a ratio. (b) Calculate the direction and magnitude of the total force the seat exerts against his body. In this problem, the forces are exerted by the seat and restraining belts.

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### Problem 14

Suppose the mass of a fully loaded module in which astronauts take off from the Moon is 10,000 kg. The thrust of its engines is 30,000 N. (a) Calculate its the magnitude of acceleration in a vertical takeoff from the Moon. (b) Could it lift off from Earth? If not, why not? If it could, calculate the magnitude of its acceleration.

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### Problem 15

What net external force is exerted on a 1100-kg artillery shell fired from a battleship if the shell is accelerated at $2.40 \times 10^4 \textrm{ m/s}^2$? What is the magnitude of the force exerted on the ship by the artillery shell?

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### Problem 16

A brave but inadequate rugby player is being pushed backward by an opposing player who is exerting a force of 800 N on him. The mass of the losing player plus equipment is 90.0 kg, and he is accelerating at $1.20\textrm{ m/s}^2$ backward. (a) What is the force of friction between the losing player’s feet and the grass? (b) What force does the winning player exert on the ground to move forward if his mass plus equipment is 110 kg? (c) Draw a sketch of the situation showing the system of interest used to solve each part. For this situation, draw a free-body diagram and write the net force equation.

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### Problem 17

Two teams of nine members each engage in a tug of war. Each of the first team’s members has an average mass of 68 kg and exerts an average force of 1350 N horizontally. Each of the second team’s members has an average mass of 73 kg and exerts an average force of 1365 N horizontally. (a) What is magnitude of the acceleration of the two teams? (b) What is the tension in the section of rope between the teams?

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### Problem 18

What force does a trampoline have to apply to a 45.0-kg gymnast to accelerate her straight up at $7.50 \textrm{ m/s}^2$? Note that the answer is independent of the velocity of the gymnast—she can be moving either up or down, or be stationary.

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### Problem 19

(a) Calculate the tension in a vertical strand of spider web if a spider of mass $8.00 \times 10^{-5} \textrm{ kg}$ hangs motionless on it. (b) Calculate the tension in a horizontal strand of spider web if the same spider sits motionless in the middle of it much like the tightrope walker in Figure 4.17. The strand sags at an angle of $12^\circ$ below the horizontal. Compare this with the tension in the vertical strand (find their ratio).

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### Problem 20

Suppose a 60.0-kg gymnast climbs a rope. (a) What is the tension in the rope if he climbs at a constant speed? (b) What is the tension in the rope if he accelerates upward at a rate of $1.50 \textrm{ m/s}^2$?

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### Problem 21

Show that, as stated in the text, a force $F_{\bot}$, exerted on a flexible medium at its center and perpendicular to its length (such as on the tightrope wire in Figure 4.17) gives rise to a tension of magnitude $T = \dfrac{F_{\bot}}{2\sin\theta}$

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### Problem 22

Consider the baby being weighed in Figure 4.34. (a) What is the mass of the child and basket if a scale reading of 55 N is observed? (b) What is the tension $T_1$ in the cord attaching the baby to the scale? (c) What is the tension $T_2$ in the cord attaching the scale to the ceiling, if the scale has a mass of 0.500 kg? (d) Draw a sketch of the situation indicating the system of interest used to solve each part. The masses of the cords are negligible.

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### Problem 23

A $5.00 \times 10^5 \textrm{ kg}$ rocket is accelerating straight up. Its engines produce $1.250 \times 10^7 \textrm{ N}$ of thrust, and air resistance is $4.50 \times 10^6 \textrm{ N}$. What is the rocket’s acceleration? Explicitly show how you follow the steps in the Problem-Solving Strategy for Newton’s laws of motion.

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### Problem 24

The wheels of a midsize car exert a force of 2100 N backward on the road to accelerate the car in the forward direction. If the force of friction including air resistance is 250 N and the acceleration of the car is $1.80 \textrm{ m/s}^w$ , what is the mass of the car plus its occupants? Explicitly show how you follow the steps in the Problem-Solving Strategy for Newton’s laws of motion. For this situation, draw a free-body diagram and write the net force equation.

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### Problem 25

Calculate the force a 70.0-kg high jumper must exert on the ground to produce an upward acceleration 4.00 times the acceleration due to gravity. Explicitly show how you follow the steps in the Problem-Solving Strategy for Newton’s laws of motion.

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### Problem 26

When landing after a spectacular somersault, a 40.0-kg gymnast decelerates by pushing straight down on the mat. Calculate the force she must exert if her deceleration is 7.00 times the acceleration due to gravity. Explicitly show how you follow the steps in the Problem-Solving Strategy for Newton’s laws of motion.

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### Problem 27

A freight train consists of two $8.00 \times 10^4 \textrm{ kg}$ engines and 45 cars with average masses of $5.50 \times 10^4 \textrm{ kg}$. (a) What force must each engine exert backward on the track to accelerate the train at a rate of $5.00 \times 10^{-2} \textrm{ m/s}^2$ if the force of friction is $7.50 \times 10^5 \textrm{ N}$, assuming the engines exert identical forces? This is not a large frictional force for such a massive system. Rolling friction for trains is small, and consequently trains are very energy-efficient transportation systems. (b) What is the force in the coupling between the 37th and 38th cars (this is the force each exerts on the other), assuming all cars have the same mass and that friction is evenly distributed among all of the cars and engines?

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### Problem 28

Commercial airplanes are sometimes pushed out of the passenger loading area by a tractor. (a) An 1800-kg tractor exerts a force of $1.75\times 10^{4}\textrm{ N}$ backward on the pavement, and the system experiences forces resisting motion that total 2400 N. If the acceleration is $0.150 \textrm{ m/s}^2$, what is the mass of the airplane? (b) Calculate the force exerted by the tractor on the airplane, assuming 2200 N of the friction is experienced by the airplane. (c) Draw two sketches showing the systems of interest used to solve each part, including the free-body diagrams for each.

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### Problem 29

A 1100-kg car pulls a boat on a trailer. (a) What total force resists the motion of the car, boat, and trailer, if the car exerts a 1900-N force on the road and produces an acceleration of $0.550 \textrm{ m/s}^2$? The mass of the boat plus trailer is 700 kg. (b) What is the force in the hitch between the car and the trailer if 80% of the resisting forces are experienced by the boat and trailer?

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### Problem 30

(a) Find the magnitudes of the forces $\vec{F_1}$ and $\vec{F_2}$ that add to give the total force $\vec{F_{\textrm{tot}}}$ shown in Figure 4.35. This may be done either graphically or by using trigonometry. (b) Show graphically that the same total force is obtained independent of the order of addition of $\vec{F_1}$ and $\vec{F_2}$ . (c) Find the direction and magnitude of some other pair of vectors that add to give $\vec{F_{\textrm{tot}}}$ . Draw these to scale on the same drawing used in part (b) or a similar picture.

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### Problem 31

Two children pull a third child on a snow saucer sled exerting forces $F_1$ and $F_2$ as shown from above in Figure 4.36. Find the acceleration of the 49.00-kg sled and child system. Note that the direction of the frictional force is unspecified; it will be in the opposite direction of the sum of $F_1$ and $F_2$.

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### Problem 32

Suppose your car was mired deeply in the mud and you wanted to use the method illustrated in Figure 4.37 to pull it out. (a) What force would you have to exert perpendicular to the center of the rope to produce a force of 12,000 N on the car if the angle is $2.00^\circ$? In this part, explicitly show how you follow the steps in the Problem-Solving Strategy for Newton’s laws of motion. (b) Real ropes stretch under such forces. What force would be exerted on the car if the angle increases to $7.00^\circ$ and you still apply the force found in part (a) to its center?

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### Problem 33

What force is exerted on the tooth in Figure 4.38 if the tension in the wire is 25.0 N? Note that the force applied to the tooth is smaller than the tension in the wire, but this is necessitated by practical considerations of how force can be applied in the mouth. Explicitly show how you follow steps in the Problem-Solving Strategy for Newton’s laws of motion.

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### Problem 34

Figure 4.39 shows Superhero and Trusty Sidekick hanging motionless from a rope. Superhero’s mass is 90.0 kg, while Trusty Sidekick’s is 55.0 kg, and the mass of the rope is negligible. (a) Draw a free-body diagram of the situation showing all forces acting on Superhero, Trusty Sidekick, and the rope. (b) Find the tension in the rope above Superhero. (c) Find the tension in the rope between Superhero and Trusty Sidekick. Indicate on your free-body diagram the system of interest used to solve each part.

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### Problem 35

A nurse pushes a cart by exerting a force on the handle at a downward angle $35.0^\circ$ below the horizontal. The loaded cart has a mass of 28.0 kg, and the force of friction is 60.0 N. (a) Draw a free-body diagram for the system of interest. (b) What force must the nurse exert to move at a constant velocity?

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### Problem 38

A 1100-kg car pulls a boat on a trailer. (a) What total force resists the motion of the car, boat, and trailer, if the car exerts a 1900-N force on the road and produces an acceleration of $1.20 \textrm{ m/s}^2$? The mass of the boat plus trailer is 700 kg. (b) What is unreasonable about the result? (c) Which premise is unreasonable, and why is it unreasonable?

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### Problem 39

(a) What is the initial acceleration of a rocket that has a mass of 1.50 \times 10^6 \textrm{ kg}$at takeoff, the engines of which produce a thrust of$2.00 \times 10^6 \textrm{ N}\$? Do not neglect gravity. (b) What is unreasonable about the result? (This result has been unintentionally achieved by several real rockets.) (c) Which premise is unreasonable, or which premises are inconsistent? (You may find it useful to compare this problem to the rocket problem earlier in this section.)

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### Problem 40

A flea jumps by exerting a force of $1.20 \times 10^{-5} \textrm{ N}$ straight down on the ground. A breeze blowing on the flea parallel to the ground exerts a force of $0.500 \times 10^{-6}\textrm{ N}$ on the flea. Find the direction and magnitude of the acceleration of the flea if its mass is $6.00 \times 10^{-7}\textrm{ kg}$. Do not neglect the gravitational force.

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### Problem 41

Two muscles in the back of the leg pull upward on the Achilles tendon, as shown in Figure 4.40. (These muscles are called the medial and lateral heads of the gastrocnemius muscle.) Find the magnitude and direction of the total force on the Achilles tendon. What type of movement could be caused by this force?

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### Problem 42

A 76.0-kg person is being pulled away from a burning building as shown in Figure 4.41. Calculate the tension in the two ropes if the person is momentarily motionless. Include a free-body diagram in your solution.

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### Problem 43

A 35.0-kg dolphin decelerates from 12.0 to 7.50 m/s in 2.30 s to join another dolphin in play. What average force was exerted to slow him if he was moving horizontally? (The gravitational force is balanced by the buoyant force of the water.)

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### Problem 44

Integrated Concepts When starting a foot race, a 70.0-kg sprinter exerts an average force of 650 N backward on the ground for 0.800 s. (a) What is his final speed? (b) How far does he travel?

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### Problem 45

Integrated Concepts A large rocket has a mass of $2.00 \times 10^6 \textrm{ kg}$ at takeoff, and its engines produce a thrust of $3.50 \times 10^7 \textrm{ N}$. (a) Find its initial acceleration if it takes off vertically. (b) How long does it take to reach a velocity of 120 km/h straight up, assuming constant mass and thrust? (c) In reality, the mass of a rocket decreases significantly as its fuel is consumed. Describe qualitatively how this affects the acceleration and time for this motion.

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### Problem 46

Integrated Concepts: A basketball player jumps straight up for a ball. To do this, he lowers his body 0.300 m and then accelerates through this distance by forcefully straightening his legs. This player leaves the floor with a vertical velocity sufficient to carry him 0.900 m above the floor. (a) Calculate his velocity when he leaves the floor. (b) Calculate his acceleration while he is straightening his legs. He goes from zero to the velocity found in part (a) in a distance of 0.300 m. (c) Calculate the force he exerts on the floor to do this, given that his mass is 110 kg.

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### Problem 47

Integrated Concepts: A 2.50-kg fireworks shell is fired straight up from a mortar and reaches a height of 110 m. (a) Neglecting air resistance (a poor assumption, but we will make it for this example), calculate the shell’s velocity when it leaves the mortar. (b) The mortar itself is a tube 0.450 m long. Calculate the average acceleration of the shell in the tube as it goes from zero to the velocity found in (a). (c) What is the average force on the shell in the mortar? Express your answer in newtons and as a ratio to the weight of the shell.

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### Problem 48

Integrated Concepts A 2.50-kg fireworks shell is fired by a mortar at an angle $10.0^\circ$ from the vertical and reaches a height of 110 m. (a) Neglecting air resistance (a poor assumption, but we will make it for this example), calculate the shell’s velocity when it leaves the mortar. (b) The mortar itself is a tube 0.450 m long. Calculate the average acceleration of the shell in the tube as it goes from zero to the velocity found in (a). (c) What is the average force on the shell in the mortar? Express your answer in newtons and as a ratio to the weight of the shell.

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### Problem 49

Integrated Concepts An elevator filled with passengers has a mass of 1700 kg. (a) The elevator accelerates upward from rest at a rate of $1.20 \textrm{ m/s}^2$ for 1.50 s. Calculate the tension in the cable supporting the elevator. (b) The elevator continues upward at constant velocity for 8.50 s. What is the tension in the cable during this time? (c) The elevator decelerates at a rate of $0.600 \textrm{ m/s}^2$ for 3.00 s. What is the tension in the cable during deceleration? (d) How high has the elevator moved above its original starting point, and what is its final velocity?

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### Problem 50

Unreasonable Results (a) What is the final velocity of a car originally traveling at 50.0 km/h that decelerates at a rate of $0.400 \textrm{ m/s}^2$ for 50.0 s? (b) What is unreasonable about the result? (c) Which premise is unreasonable, or which premises are inconsistent?

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### Problem 51

Unreasonable Results: A 75.0-kg man stands on a bathroom scale in an elevator that accelerates from rest to 30.0 m/s in 2.00 s. (a) Calculate the scale reading in newtons and compare it with his weight. (The scale exerts an upward force on him equal to its reading.) (b) What is unreasonable about the result? (c) Which premise is unreasonable, or which premises are inconsistent?

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### Problem 52

(a) What is the strength of the weak nuclear force relative to the strong nuclear force? (b) What is the strength of the weak nuclear force relative to the electromagnetic force? Since the weak nuclear force acts at only very short distances, such as inside nuclei, where the strong and electromagnetic forces also act, it might seem surprising that we have any knowledge of it at all. We have such knowledge because the weak nuclear force is responsible for beta decay, a type of nuclear decay not explained by other forces.

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### Problem 53

(a) What is the ratio of the strength of the gravitational force to that of the strong nuclear force? (b) What is the ratio of the strength of the gravitational force to that of the weak nuclear force? (c) What is the ratio of the strength of the gravitational force to that of the electromagnetic force? What do your answers imply about the influence of the gravitational force on atomic nuclei?

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### Problem 54

What is the ratio of the strength of the strong nuclear force to that of the electromagnetic force? Based on this ratio, you might expect that the strong force dominates the nucleus, which is true for small nuclei. Large nuclei, however, have sizes greater than the range of the strong nuclear force. At these sizes, the electromagnetic force begins to affect nuclear stability. These facts will be used to explain nuclear fusion and fission later in this text.

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### Problem 1 (AP)

Figure 4.42 represents a racetrack with semicircular sections connected by straight sections. Each section has length d, and markers along the track are spaced d/4 apart. Two people drive cars counterclockwise around the track, as shown. Car X goes around the curves at constant speed vc, increases speed at constant acceleration for half of each straight section to reach a maximum speed of 2vc, then brakes at constant acceleration for the other half of each straight section to return to speed vc. Car Y also goes around the curves at constant speed vc, increases its speed at constant acceleration for one-fourth of each straight section to reach the same maximum speed 2vc, stays at that speed for half of each straight section, then brakes at constant acceleration for the remaining fourth of each straight section to return to speed vc.

(a) On the figures below, draw an arrow showing the direction of the net force on each of the cars at the positions noted by the dots. If the net force is zero at any position, label the dot with 0. Description of Figure 4.43:

• The first dot on the left center of the track is at the same position as it is on the Car X track.
• The second dot is just slight to the right of the Car X dot (less than a dash) past three perpendicular hash marks moving to the right.
• The third dot is about one and two-thirds perpendicular hash marks to the right of the center top perpendicular has mark.
• The fourth dot is in the same position as the Car X figure (one perpendicular hash mark above the center right perpendicular hash mark).
• The fifth dot is about one and two-third perpendicular hash marks to the right of the center bottom perpendicular hash mark.
• The sixth dot is in the same position as the Car Y dot (one and two third perpendicular hash marks to the left of the center bottom hash mark).

(b) i. Indicate which car, if either, completes one trip around the track in less time, and justify your answer qualitatively without using equations.

ii. Justify your answer about which car, if either, completes one trip around the track in less time quantitatively with appropriate equations.

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### Problem 4 (AP)

What causes the force that moves a boat forward when someone rows it?
1. The force is caused by the rower’s arms.
2. The force is caused by an interaction between the oarsand gravity.
3. The force is caused by an interaction between the oars and the water the boat is traveling in.
4. The force is caused by friction.

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### Problem 6 (AP)

A ball with a mass of 0.25 kg hits a gym ceiling with a force of 78.0 N. What happens next?
1. The ball accelerates downward with a force of 80.5 N.
2. The ball accelerates downward with a force of 78.0 N.
3. The ball accelerates downward with a force of 2.45 N.
4. It depends on the height of the ceiling.

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### Problem 7 (AP)

Which of the following is true?

1. Earth exerts a force due to gravity on your body, and

your body exerts a smaller force on the Earth, because

your mass is smaller than the mass of the Earth.

2. The Moon orbits the Earth because the Earth exerts a

force on the Moon and the Moon exerts a force equal in

magnitude and direction on the Earth.

3. A rocket taking off exerts a force on the Earth equal to

the force the Earth exerts on the rocket.

4. An airplane cruising at a constant speed is not affected

by gravity.

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### Problem 8 (AP)

Stationary skater A pushes stationary skater B, who then 2 accelerates at $5.0\textrm{ m/s}^2$ . Skater A does not move. Since forces act in action-reaction pairs, explain why Skater A did not move?

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### Problem 9 (AP)

The current in a river exerts a force of 9.0 N on a balloon floating in the river. A wind exerts a force of 13.0 N on the balloon in the opposite direction. Draw a free-body diagram to show the forces acting on the balloon. Use your free-body diagram to predict the effect on the balloon.

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### Problem 10 (AP)

A force is applied to accelerate an object on a smooth icy surface. When the force stops, which of the following will be true? (Assume zero friction.)
1. The object’s acceleration becomes zero.
2. The object’s speed becomes zero.
3. The object’s acceleration continues to increase at a constant rate.
4. The object accelerates, but in the opposite direction.

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### Problem 11 (AP)

A parachutist’s fall to Earth is determined by two opposing forces. A gravitational force of 539 N acts on the parachutist. After 2 s, she opens her parachute and experiences an air resistance of 615 N. At what speed is the parachutist falling after 10 s?

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### Problem 12 (AP)

A flight attendant pushes a cart down the aisle of a plane in flight. In determining the acceleration of the cart relative to the plane, which factor do you not need to consider?
1. The friction of the cart’s wheels.
2. The force with which the flight attendant’s feet push on the floor.
3. The velocity of the plane.
4. The mass of the items in the cart.

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### Problem 13 (AP)

A landscaper is easing a wheelbarrow full of soil down a hill. Define the system you would analyze and list all the forces that you would need to include to calculate the acceleration of the wheelbarrow.

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### Problem 14 (AP)

Two water-skiers, with masses of 48 kg and 61 kg, are preparing to be towed behind the same boat. When the boat accelerates, the rope the skiers hold onto accelerates with it and exerts a net force of 290 N on the skiers. At what rate will the skiers accelerate?
1. $10.8 \textrm{ m/s}^2$
2. $2.7 \textrm{ m/s}^2$
3. $6.0\textrm{ m/s}^2$ and $4.8 \textrm{ m/s}^2$
4. $5.3 \textrm{ m/s}^2$

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### Problem 15 (AP)

A figure skater has a mass of 40 kg and her partner's mass is 50 kg. She pushes against the ice with a force of 120 N, causing her and her partner to move forward. Calculate the pair’s acceleration. Assume that all forces opposing the motion, such as friction and air resistance, total 5.0 N.

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### Problem 16 (AP)

An archer shoots an arrow straight up with a force of 24.5 N. The arrow has a mass of 0.4 kg. What is the force of gravity on the arrow?
1. $9.8 \textrm{m/s}^2$
2. $9.8 \textrm{ N}$
3. $61.25 \textrm{ N}$
4. $3.9 \textrm{ N}$

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### Problem 19 (AP)

Two teams are engaging in a tug–of-war. The rope suddenly snaps. Which statement is true about the forces involved?

1. The forces exerted by the two teams are no longer equal; the teams will accelerate in opposite directions as a result.

2. The forces exerted by the players are no longer balanced by the force of tension in the rope; the teams will accelerate in opposite directions as a result.

3. The force of gravity balances the forces exerted by the players; the teams will fall as a result

4. The force of tension in the rope is transferred to the players; the teams will accelerate in opposite directions as a result.

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### Problem 20 (AP)

The following free-body diagram represents a toboggan on a hill. What acceleration would you expect, and why?
1. Acceleration down the hill; the force due to being pushed, together with the downhill component of gravity, overcomes the opposing force of friction.
2. Acceleration down the hill; friction is less than the opposing component of force due to gravity.
3. No movement; friction is greater than the force due to being pushed.
4. It depends on how strong the force due to friction is.

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### Problem 22 (AP)

A car is sliding down a hill with a slope of $20^\circ$. The mass of the car is 965 kg. When a cable is used to pull the car up the slope, a force of 4215 N is applied. What is the car’s acceleration, ignoring friction?

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### Problem 23 (AP)

A toboggan with two riders has a total mass of 85.0 kg. A third person is pushing the toboggan with a force of 42.5 N at the top of a hill with an angle of 15°. The force of friction on the toboggan is 31.0 N. Which statement describes an accurate free-body diagram to represent the situation?

1. An arrow of magnitude 10.5 N points down the slope of the hill.

2. An arrow of magnitude 833 N points straight down.

3. An arrow of magnitude 833 N points perpendicular to the slope of the hill.

4. An arrow of magnitude 73.5 N points down the slope of the hill.

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### Problem 24 (AP)

A mass of 2.0 kg is suspended from the ceiling of an elevator by a rope. What is the tension in the rope when the elevator (i) accelerates upward at $1.5 \textrm{ m/s}^2$? (ii) accelerates downward at $1.5 \textrm{ m/s}^2$?
1. (i) 22.6 N; (ii) 16.6 N
2. Because the mass is hanging from the elevator itself, the tension in the rope will not change in either case.
3. (i) 22.6 N; (ii) 19.6 N
4. (i) 16.6 N; (ii) 19.6 N

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### Problem 25 (AP)

Which statement is true about drawing free-body diagrams?

1. Drawing a free-body diagram should be the last step in solving a problem about forces.

2. Drawing a free-body diagram helps you compare forces quantitatively.

3. The forces in a free-body diagram should always balance.

4. Drawing a free-body diagram can help you determine the net force.

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### Problem 27 (AP)

Two people push on a boulder to try to move it. The mass of the boulder is 825 kg. One person pushes north with a force of 64 N. The other pushes west with a force of 38 N. Predict the magnitude of the acceleration of the boulder. Assume that friction is negligible.

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### Problem 28 (AP)

The figure shows the forces exerted on a block that is sliding on a horizontal surface: the gravitational force of 40 N, the 40 N normal force exerted by the surface, and a frictional force exerted to the left. The coefficient of friction between the block and the surface is 0.20. The acceleration of the block is most nearly
1. $1.0 \textrm{ m/s}^2$ to the right
2. $1.0 \textrm{ m/s}^2$ to the left
3. $2.0 \textrm{ m/s}^2$ to the right
4. $2.0 \textrm{ m/s}^2$ to the left

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### Problem 31 (AP)

Which of the basic forces best explains tension in a rope being pulled between two people? Is the acting force causing attraction or repulsion in this instance?
1. gravity; attraction

2. electromagnetic; attraction

3. weak and strong nuclear; attraction

4. weak and strong nuclear; repulsion

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### Problem 33 (AP)

The gravitational force is the weakest of the four basic forces. In which case can the electromagnetic, strong, and weak forces be ignored because the gravitational force is so strongly dominant?
1. a person jumping on a trampoline

2. a rocket blasting off from Earth

3. a log rolling down a hill

4. all of the above

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