University Physics for the Physical and Life Sciences Volume 1

Philip R Kesten, David L Tauck

Chapter 4

Newton’s Laws of Motion - all with Video Answers

Educators

Chapter Questions

Problem 1

According to Newton's second law, does the direction of the net force always equal the direction of the acceleration? SSM

Prabhu Ramji

Prabhu Ramji

Numerade Educator

Problem 2

If the sum of the forces acting on an object equals zero, does this imply that the object is at rest?

Prabhu Ramji

Numerade Educator

Problem 3

Calc What are the basic SI units $(\mathrm{kg}, \mathrm{m}, \mathrm{s})$ for force according to Newton's second law?
$$
\sum F=m a
$$
How do the units compare with the differential form of this law?
$$
\sum F=\frac{d(m v)}{d t}
$$

Prabhu Ramji

Numerade Educator

Problem 4

Medical, Sports Gymnastics routines are done over a padded floor to protect athletes who fall. Why is falling on padding safer than falling on concrete?

Prabhu Ramji

Numerade Educator

Problem 5

A definition of the inertia of an object is that it is a measure of the quantity of matter. How does this definition compare with the definition discussed in the chapter?

Prabhu Ramji

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Problem 6

$\bullet$ Wen constructing a free-body diagram, why is it a good idea to choose your coordinate system so that the motion of an object is along one of the axes?

Prabhu Ramji

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Problem 7

A certain rope will break under any tension greater than $800 \mathrm{~N}$. How can it be used to lower an object weighing $850 \mathrm{~N}$ over the edge of a cliff without it breaking? SSM

Prabhu Ramji

Numerade Educator

Problem 8

-Sports A boxer claims that Newton's third law helps him while boxing. He says that during a boxing match, the force that his jaw feels is the same as the force that his opponent's fist feels (when the opponent is doing the punching). Therefore, his opponent will feel the same force as he feels and he will be able to fight on without any problems, no matter how many punches he receives or gives. It will always be an "even fight." Discuss any flaws in his reasoning.

Linda Winkler

Numerade Educator

Problem 9

Astro We know that the Sun pulls on Earth. Does Earth also pull on the Sun? Why or why not? SSM

Prabhu Ramji

Numerade Educator

Problem 10

Sports How can a fisherman land a 5 -lb fish using fishing line that is rated at $4 \mathrm{lb}$ ?

Prabhu Ramji

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Problem 11

Tension is a very common force in day-to-day life. Identify five ordinary situations that involve the force of tension.

Prabhu Ramji

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Problem 12

Explain why the force that a surface exerts on an object that rests on it is called the normal force.

Prabhu Ramji

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Problem 13

A chair is mounted on a scale inside an elevator in the physics building at the University of California, Davis. Describe the variation in the scale reading as the elevator begins to ascend, goes up at constant speed, stops, begins to descend, goes down at a constant speed, and stops again.

Prabhu Ramji

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Problem 14

List all the forces acting on a soft-drink can if it were sitting on your desk.

Prabhu Ramji

Numerade Educator

Problem 15

What is the net force on a bathroom scale when a 75 -kg person stands on it? SSM

Prabhu Ramji

Numerade Educator

Problem 16

An object of mass $m$ is being weighed in an elevator which is moving upward with an acceleration $a$. What is the result if the weighing is done using (a) a spring balance and (b) a pan balance?

Matthew Miranda

Matthew Miranda

Numerade Educator

Problem 17

Two forces of $30 \mathrm{~N}$ and $70 \mathrm{~N}$ act on an object. What are the minimum and maximum values for the sum of these two forces?

Prabhu Ramji

Numerade Educator

Problem 18

You apply a $60-\mathrm{N}$ force to push a box across the floor at constant speed. If you increase the applied force to $80 \mathrm{~N}$, will the box speed up to some new constant speed or will it continue to speed up indefinitely? Assume that the floor is horizontal and the surface is uniform. Explain your answer.

Prabhu Ramji

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Problem 19

Astro Why would it be easier to lift a truck on the Moon's surface than it is on Earth? SSM

Prabhu Ramji

Numerade Educator

Problem 20

Medical Why should the driver and passengers in a car wear seatbelts? Explain your answer.

Ivan Kochetkov

Numerade Educator

Problem 21

Medical Why does the American Academy of Pediatrics recommend that all infants sit in rear-facing car seats starting with their first ride home from the hospital? Explain your answer.

Ivan Kochetkov

Numerade Educator

Problem 22

Medical Use Newton's third law to explain the forces involved in walking.

Prabhu Ramji

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Problem 23

Biology Use Newton's third law to explain how birds are able to fly forward. SSM

Prabhu Ramji

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Problem 24

Medical A car stops suddenly during a head-on collision, causing the driver's brain to slam into the skull. The resulting injury would most likely be to which part of the brain?
A. Frontal portion of the brain
B. Rear portion of the brain
C. Middle portion of the brain
D. Left side of the brain
E. Right side of the brain

Prabhu Ramji

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Problem 25

Medical During the sudden impact of a car accident, a person's neck can experience abnormal forces, resulting in an injury commonly known as whiplash. If a victim's head and neck move in the manner shown in Figure 4-34, his car was hit from the
A. front.
B. rear.
C. right side.
D. left side.
E. top during a rollover. $S S M$

Prabhu Ramji

Numerade Educator

Problem 26

The net force on a moving object suddenly becomes zero and remains zero. The object will
A. stop abruptly.
B. reduce speed gradually.
C. continue at constant velocity.
D. increase speed gradually.
E. reduce speed abruptly.

Prabhu Ramji

Numerade Educator

Problem 27

Which has greater monetary value, a newton of gold on Earth or a newton of gold on the Moon?
A. The newton of gold on Earth
B. The newton of gold on the Moon
C. The value is the same, regardless of location
D. One cannot say without checking the weight on the Moon.
E. The newton of gold on the Moon but only when inside a spaceship.

Prabhu Ramji

Numerade Educator

Problem 28

According to Newton's second law of motion, when a net force acts on an object, the acceleration is
A. zero.
B. inversely proportional to the object's mass.
C. independent of mass.
D. inversely proportional to the net force.
E. Both options (A) and (B) are correct.

Prabhu Ramji

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Problem 29

When a net force acts on an object, it
A. is at rest.
B. is in motion with a constant velocity.
C. has zero speed.
D. is accelerating.
E. is decelerating.

Prabhu Ramji

Numerade Educator

Problem 30

In the absence of a net force, an object cannot be A. at rest.
B. in motion with a constant velocity.
C. accelerating.
D. moving with an acceleration of zero.
E. experiencing opposite but equal forces.

Prabhu Ramji

Numerade Educator

Problem 31

In the absence of a net force, an object can be A. at rest.
B. in motion with a constant velocity.
C. accelerating.
D. at rest or in motion with a constant velocity.
E. It's not possible to know without more information. SSM

Prabhu Ramji

Numerade Educator

Problem 32

Elevators decelerate to stop at a floor. During the deceleration of an elevator traveling upward, the normal force on the feet of a passenger is her weight. During the deceleration of an elevator traveling downward, the normal force on the feet of a passenger is his weight.
A. larger than; smaller than
B. larger than; larger than
C. smaller than; smaller than
D. smaller than; larger than
E. equal to; equal to

Prabhu Ramji

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Problem 33

How does the magnitude of the normal force exerted by the ramp in Figure 4-35 compare to the weight of the block?
A. Equal to the weight of the block
B. Greater than the weight of the block
C. Less than the weight of the block
D. Possibly greater than or less than the weight of the block, depending on whether or not the ramp surface is smooth
E. Possibly greater than or equal to the weight of the block, depending on whether or not the ramp surface is smooth

Prabhu Ramji

Numerade Educator

Problem 34

Case (a) in Figure 4-36 is a block that is accelerated across a frictionless table by a hanging $10-\mathrm{N}$ block $(1.02 \mathrm{~kg})$. In case $(b)$, the same block is accelerated by a steady $10-\mathrm{N}$ tension in the string. Treat the masses of the strings as negligible. The block's acceleration in case (b) is
A. greater than its acceleration in case (a).
B. less than its acceleration in case (a).
C. equal to its acceleration in case (a).
D. twice its acceleration in case (a).
E. half its acceleration in case (a).

Ivan Kochetkov

Numerade Educator

Problem 35

Estimate the weight of hve common objects using newtons (not pounds or ounces).

Prabhu Ramji

Numerade Educator

Problem 36

Estimate the normal force acting on an apple that rests on a flat surface. What would this estimate be if the surface were tilted at an incline of $30^{\circ}$ with the horizontal?

Prabhu Ramji

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Problem 37

Give an estimate of the force that a major league baseball pitcher exerts on a baseball when he throws it. SSM

Prabhu Ramji

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Problem 38

Estimate the maximum tension in the cable that supports a typical elevator.

Prabhu Ramji

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Problem 39

Estimate the force imparted on a tennis ball as it is fired from a tennis ball machine.

Prabhu Ramji

Numerade Educator

Problem 40

Estimate the tension in a rope that pulls you on water skis at a constant speed behind a speedboat.

Linda Winkler

Numerade Educator

Problem 41

Estimate the force that is produced with the "jaws of life" (the pneumatic tool used to rip open the jammed doors of a vehicle that is involved in an accident).

Linda Winkler

Numerade Educator

Problem 42

Estimate the force in newtons required to flip on a light switch.

Linda Winkler

Numerade Educator

Problem 43

Estimate the force in newtons associated with snapping your fingers.

Linda Winkler

Numerade Educator

Problem 44

Medical During an arthroscopic surgery repair of a patient's knee, a portion of healthy tendon is grafted in place of a damaged anterior cruciate ligament (ACL). To test the results, the surgeon applies a known force to the ligament and increases it at $1-\mathrm{s}$ intervals for $10 \mathrm{~s}$. Plot the data listed in the table as a function of time in a spreadsheet or on a graphing calculator, draw the best fit line, and use the equation of the line to estimate the force that would correspond to a time of $20 \mathrm{~s}$.

Linda Winkler

Numerade Educator

Problem 45

Use a spreadsheet or graphing calculator to plot the velocity versus height of an express elevator. The elevator starts from rest on the ground floor, accelerates up to its maximum speed of $10 \mathrm{~m} / \mathrm{s}$ after reaching the 4th floor (the distance between each floor is $3.5 \mathrm{~m}$ ), remains at this speed until the 20th floor, and then stops at the 30th floor. Identify the point(s) on the graph when the weight of a rider will reach its maximum value. SSM

Linda Winkler

Numerade Educator

Problem 46

The graph in Figure 4-37 shows the force applied to a $2.5-\mathrm{kg}$ object as a function of time. Calculate the velocity of the object at $t=1 \mathrm{~s}$ and $t=4 \mathrm{~s}$. Assume the object starts from rest.

Sachin Rao

Numerade Educator

Problem 47

What is the acceleration of a $2000-\mathrm{kg}$ car if the net force on the car is $4000 \mathrm{~N}$ ?

Mayukh Banik

Numerade Educator

Problem 48

What net force is needed to accelerate a $2000-\mathrm{kg}$ car at $2 \mathrm{~m} / \mathrm{s}^{2}$ ?

Mayukh Banik

Numerade Educator

Problem 49

Suppose that the engine of a car delivers a maximum force of $15,000 \mathrm{~N}$. In the absence of any other forces, what is the maximum acceleration this force can produce in a $1250-\mathrm{kg}$ car? SSM

Prabhu Ramji

Numerade Educator

Problem 50

$\bullet$ Applying a constant force to an object causes it to accelerate at $10 \mathrm{~m} / \mathrm{s}^{2}$. What will the acceleration of the object be if (a) the force is doubled, (b) the mass is halved, (c) the force is doubled and the mass is doubled, (d) the force is doubled and the mass is halved, (e) the force is halved, (f) the mass is doubled, (g) the force is halved and the mass is halved, and ( $h)$ the force is halved and the mass is doubled?

Prabhu Ramji

Numerade Educator

Problem 51

What is the weight on Earth of a wrestler who has a mass of $120 \mathrm{~kg}$ ?

Prabhu Ramji

Numerade Educator

Problem 52

A wrestler has a mass of $120 \mathrm{~kg}$. What are (a) his mass and (b) weight on the Moon, where $g$ is $1.62 \mathrm{~m} / \mathrm{s}^{2}$ ?

Sachin Rao

Numerade Educator

Problem 53

A bluefin tuna has a mass of $250 \mathrm{~kg}$. What is its weight? SSM

Prabhu Ramji

Numerade Educator

Problem 54

(a) How does your mass differ as measured in Mexico City versus Los Angeles? (b) In which city is your weight greater?

Samuel Smith

Numerade Educator

Problem 55

An astronaut has a mass of $80 \mathrm{~kg}$. How much would the astronaut weigh on Mars where surface gravity is $38 \%$ of that on Earth?

Prabhu Ramji

Numerade Educator

Problem 56

Draw a free-body diagram for a heavy crate being lowered by a steel cable straight down at a constant speed.

Prabhu Ramji

Numerade Educator

Problem 57

Draw a free-body diagram for a person pushing a box across a smooth floor at a steadily increasing speed. Ignore the friction between the box and the smooth floor. SSM

Prabhu Ramji

Numerade Educator

Problem 58

Draw a free-body diagram for a bicycle rolling down a hill. Ignore the friction between the bicycle wheels and the hill, but consider any air resistance.

Prabhu Ramji

Numerade Educator

Problem 59

A tugboat uses its winch to pull up a sinking sailboat with an upward force of $4500 \mathrm{~N}$. The mass of the boat is $200 \mathrm{~kg}$ and the water acts on the sailboat with a drag force of $2000 \mathrm{~N}$. Draw a free-body diagram for the sailboat and describe the motion of the sailboat.

Prabhu Ramji

Numerade Educator

Problem 60

Two forces are applied to a block of mass $M$ equal to $14 \mathrm{~kg}$ that sits on a horizontal, frictionless table. One force $\vec{F}_{1}$ has a magnitude of $10 \mathrm{~N}$ and is directed at an angle $\theta_{1}$ equal to $37^{\circ}$ from the $x$ direction as labeled in Figure 4-38. As a result of the forces, the block experiences an acceleration $a$ equal to $0.5 \mathrm{~m} / \mathrm{s}^{2}$ in the $x$ direction only. (a) Find the $x$ and $y$ components of the second force. (b) Draw the second force in its correct position and to scale in the picture.

Guilherme Barros

Guilherme Barros

Numerade Educator

Problem 61

Three rugby players are pulling horizontally on ropes attached to a box, which remains stationary. Player 1 exerts a force $F_{1}$ equal to $100 \mathrm{~N}$ at an angle $\theta_{1}$ equal to $60^{\circ}$ with respect to the $+x$ direction (Figure 4-39). Player 2 exerts a force $F_{2}$ equal to $200 \mathrm{~N}$ at an angle $\theta_{2}$ equal to $37^{\circ}$ with respect to the $+x$ direction. The view in the figure is from above. Ignore friction and note that gravity plays no role in this problem! SSM (a) Find the force $F_{3}$ exerted by Player 3 . State your answer by giving the components of $F_{3}$ in the directions perpendicular to and parallel to the positive $x$ direction. (b) Redraw the diagram and add the force $F_{3}$ as carefully as you can. (c) Player 3 's rope breaks, and Player 2 adjusts by pulling with $F_{2}$ equal to $150 \mathrm{~N}$ at the same angle as before. In which direction is the acceleration of the box, relative to the direction shown? (d) In part (c), the acceleration is measured to be $10 \mathrm{~m} / \mathrm{s}^{2}$. What is the mass of the box?

Linda Winkler

Numerade Educator

Problem 62

Three forces act on a $2-\mathrm{kg}$ object as shown in Figure 4-40. Find the magnitude of each force if the acceleration of the object is $1.5 \mathrm{~m} / \mathrm{s}^{2}$ toward the $+x$ direction.

Susan Hallstrom

Susan Hallstrom

Numerade Educator

Problem 63

Box A weighs $80 \mathrm{~N}$ and rests on a table (Figure 4-41). A rope that connects boxes $A$ and $B$ drapes over a pulley so that box $B$ hangs above the table, as shown in the figure. The pulley and rope are massless and the pulley is frictionless. What force does the table exert on box A if box B weighs (a) $35 \mathrm{~N}$; (b) $70 \mathrm{~N}$; (c) 90 N?

Prabhu Ramji

Numerade Educator

Problem 64

Students pull on two ropes attached to an object of mass $M$; they apply horizontal forces $F_{1}$ and $F_{2}$, respectively. Because of these forces, the object experiences an acceleration of $a$ equal to $7 \mathrm{~m} / \mathrm{s}^{2}$ in the $x$ direction, as shown in Figure 4-42. (The figure shows the object and force $F_{1}$ when viewed from above.) (a) Find the magnitude of $F_{2}$ and (b) make a careful drawing to show its direction, given $F_{1}=20 \mathrm{~N}, \theta=30^{\circ}$, and $M=3 \mathrm{~kg}$.

Donald Albin

Numerade Educator

Problem 65

A 100 kg streetlight is supported equally by two ropes as shown in Figure 4-43.
One rope pulls up and to the right, $40^{\circ}$ above the horizontal; the other rope pulls up and to the left, $40^{\circ}$ above the horizontal. Find the tension in each rope. SSM

Prabhu Ramji

Numerade Educator

Problem 66

A 200-N sign is supported by two ropes; one rope pulls up and to the right, $30^{\circ}$ above the horizontal, and the other pulls up and to the left $45^{\circ}$ above the horizontal (Figure 4-44). Find the tension in each rope.

Prabhu Ramji

Numerade Educator

Problem 67

The distance between two telephone poles is $50 \mathrm{~m}$. When a $0.50-\mathrm{kg}$ bird lands on the telephone wire midway between the poles, the wire sags $0.15 \mathrm{~m}$. How much tension does the bird produce in the wire? Ignore the weight of the wire.

Prabhu Ramji

Numerade Educator

Problem 68

A ball that has a weight of $40 \mathrm{~N}$ is falling freely toward the floor. What force does the ball exert on the

Mayukh Banik

Numerade Educator

Problem 69

A locomotive pulls 10 identical freight cars. The force between the locomotive and the first car is $100,000 \mathrm{~N}$ and the acceleration of the train is $2 \mathrm{~m} / \mathrm{s}^{2}$. There is no friction to consider. Find the force between the ninth and tenth cars. SSM

Prabhu Ramji

Numerade Educator

Problem 70

A locomotive pulls 10 identical freight cars with an acceleration of $2 \mathrm{~m} / \mathrm{s}^{2}$. How does the force between the third and fourth cars compare to the force between the seventh and eighth cars?

Prabhu Ramji

Numerade Educator

Problem 71

What is the net force on an apple that weighs $3.5 \mathrm{~N}$ when you hold it at rest in your hand?

Supratim Pal

Numerade Educator

Problem 72

A block that has a mass of $0.01 \mathrm{~kg}$ and a block that has a mass of $2 \mathrm{~kg}$ are attached to the ends of a rope. A student holds the 2-kg block and lets the 0.01-kg block hang below it, then he lets go. What is the tension in the rope while the blocks are falling, before either hits the ground? Air resistance can be neglected.

Prabhu Ramji

Numerade Educator

Problem 73

A $2-\mathrm{kg}$ object experiences the three forces shown in Figure 4-45. What is the acceleration of the object? Note that the forces are measured in newtons. SSM

Luis Rios

Numerade Educator

Problem 74

While parachuting, a 66-kg person experiences a downward acceleration of $2.5 \mathrm{~m} / \mathrm{s}^{2}$. What is the downward force on the parachute from the person?

Prabhu Ramji

Numerade Educator

Problem 75

A bicycle and $50-\mathrm{kg}$ rider accelerate at $1.0 \mathrm{~m} / \mathrm{s}^{2}$ up an incline of $10^{\circ}$ above the horizontal. What is the magnitude of the force that the bicycle exerts on the rider?

Prabhu Ramji

Numerade Educator

Problem 76

A car accelerates from 0 to $100 \mathrm{~km} / \mathrm{h}$ in $4.5 \mathrm{~s}$. What force does a $65.0-\mathrm{kg}$ passenger experience during this acceleration?

Prabhu Ramji

Numerade Educator

Problem 77

A car uniformly accelerates from 0 to $28 \mathrm{~m} / \mathrm{s}$. A $60.0$ kg passenger experiences a horizontal force of $400 \mathrm{~N}$. How much time does it take for the car to reach $28 \mathrm{~m} / \mathrm{s}$ ? SSM

Prabhu Ramji

Numerade Educator

Problem 78

Adam and Ben pull hand over hand on opposite ends of a rope while standing on a frictionless frozen pond. Adam's mass is $75 \mathrm{~kg}$ and Ben's mass is $50 \mathrm{~kg}$. If Adam's acceleration is $1 \mathrm{~m} / \mathrm{s}^{2}$ to the east, what are the magnitude and direction of Ben's acceleration?

Prabhu Ramji

Numerade Educator

Problem 79

Calc A 2-kg object moves in the $x$ direction according to the following function:
$$
x(t)=2 t^{2}+3 t-5 \quad \text { (SI units) }
$$

Lucas Finney

Numerade Educator

Problem 80

Two blocks $M_{1}$ and $M_{2}$ are connected by a massless string that passes over a massless pulley (Figure 4-46). $M_{2}$, which has a mass of $20 \mathrm{~kg}$, rests on a long ramp of angle $\theta$ equal to $30^{\circ}$. Friction can be ignored in this problem. (a) Find the value of $M_{1}$ for which the two blocks are in equilibrium (no acceleration). (b) If the actual mass of $M_{1}$ is $5 \mathrm{~kg}$ and the system is allowed to move, find the acceleration of the two blocks. (c) In part (b) does $M_{2}$ move up or down the ramp? (d) In part (b), how far does block $M_{2}$ move in 2 s?

Prabhu Ramji

Numerade Educator

Problem 81

In Figure 4-47, the block on the left incline is $6 \mathrm{~kg}$. Find the mass of the block on the right incline so that the system is in equilibrium (no acceleration). All surfaces are frictionless. SSM

Prabhu Ramji

Numerade Educator

Problem 82

A child on a sled starts from rest at the top of a $20^{\circ}$ slope. Assuming that there are no forces resisting the sled's motion, how long will the child take to reach the bottom of the slope, $210 \mathrm{~m}$ from the top?

Nishant Kumar

Numerade Educator

Problem 83

A car is proceeding at a speed of $14 \mathrm{~m} / \mathrm{s}$ when it collides with a stationary car in front. During the collision, the first car moves a distance of $0.3 \mathrm{~m}$ as it comes to a stop. The driver is wearing her seat belt, so she remains in her seat during the collision. If the driver's mass is $52 \mathrm{~kg}$, how much force does the belt exert on her during the collision?

Prabhu Ramji

Numerade Educator

Problem 84

Your friend's car runs out of fuel and you volunteer to push it to the nearest gas station. You carefully drive your car so that the bumpers of the two cars are in contact and then slowly accelerate to a speed of $2.0 \mathrm{~m} / \mathrm{s}$ over the course of $1 \mathrm{~min}$. If the mass of your friend's car is $1200 \mathrm{~kg}$, what is the contact force between the two bumpers?

Supratim Pal

Numerade Educator

Problem 85

A $30-\mathrm{kg}$ golden retriever stands on a digital scale. If the dog and scale are positioned in a elevator, calculate the weight of the dog when the elevator (a) accelerates at $3.5 \mathrm{~m} / \mathrm{s}^{2}$ downward, (b) when the elevator cruises down at a steady speed, and (c) when the elevator accelerates at

Prabhu Ramji

Numerade Educator

Problem 86

What is the weight of a rider on the Inclinator (the lift at the Luxor Hotel in Las Vegas)? Assume the weight of the person is $588 \mathrm{~N}$ when at rest and that the Inclinator moves at a constant acceleration of $1.25 \mathrm{~m} / \mathrm{s}^{2}$, in a direction $39.0^{\circ}$ above the horizontal. Assume that the rider stands vertically in the elevator car.

Prabhu Ramji

Numerade Educator

Problem 87

Describe the variation in the weight of a rider on an elevator that initially starts from rest, accelerates upward at $3 \mathrm{~m} / \mathrm{s}^{2}$, cruises upward at $4 \mathrm{~m} / \mathrm{s}$, slows to a stop at $2 \mathrm{~m} / \mathrm{s}^{2}$, then free-falls all the way to the bottom of the elevator shaft before striking springs that bring the car to a safe stop. Assume the rider has a stationary weight of $700 \mathrm{~N}$.

Prabhu Ramji

Numerade Educator

Problem 88

Calc The speed of an object that has mass $m$ moving along the $x$ axis is given by the following function:
$$
v(x)=b x^{2}
$$
where $b=8 /(\mathrm{s} \cdot \mathrm{m})$. (a) Derive an equation for the force as a function of $x$. (Hint: Use the chain rule.) (b) Calculate the force when $m=2 \mathrm{~kg}$ and $x=10 \mathrm{~m}$.

Vishal Gupta

Numerade Educator

Problem 89

Biology On average, froghopper insects have a mass of $12.3 \mathrm{mg}$ and jump to a height of $428 \mathrm{~mm}$. The takeoff velocity is achieved as the little critter flexes its leg over a distance of approximately $2.0 \mathrm{~mm}$. Assume a vertical jump with constant acceleration. (a) How long does the jump last (the jump itself, not the time in the air), and what is the froghopper's acceleration during that time? (b) Make a free-body diagram of the froghopper during its leap (but before it leaves the ground). (c) What force did the ground exert on the froghopper during the jump? Express your answer in millinewtons and as a multiple of the insect's weight. SSM

Linda Winkler

Numerade Educator

Problem 90

Sports The tension at which a fishing line breaks is commonly called the line's "strength." A minimum strength of $300 \mathrm{~N}$ is needed to keep a line from breaking when the hook gets snagged on a floating log, which is initially drifting at $2.8 \mathrm{~m} / \mathrm{s}$. What is the mass of the log? Assume a constant deceleration.

Arpit Gupta

Numerade Educator

Problem 91

Sports A $22-g$ arrow is positioned in a bow as shown in Figure 4-48. If the tension in the bowstring is $180 \mathrm{~N}$, calculate the acceleration of the arrow when it is released. Assume the angle that is shown is $25^{\circ}$ and the tension in the string is $100 \%$ transmitted to the arrow.

Nicholas Majtenyi

Nicholas Majtenyi

Numerade Educator

Problem 92

A fuzzy die that has a weight of $1.8 \mathrm{~N}$ hangs from the ceiling of a car by a massless string. The car travels on a horizontal road and has an acceleration $2.7 \mathrm{~m} / \mathrm{s}^{2}$ to the left. The string makes an angle $\theta$ with respect to the vertical, shown in Figure 4-49. Find the angle $\theta$.

Prabhu Ramji

Numerade Educator

Problem 93

Two mountain climbers are working their way up a glacier when one falls into a crevasse (Figure 4-50). The icy slope
can be considered frictionless.
Sue's weight is pulling Paul up the $45^{\circ}$ slope. If Sue's mass

Prabhu Ramji

Numerade Educator

Problem 94

Medical A car traveling at $28 \mathrm{~m} / \mathrm{s}$ hits a bridge abutment. A passenger in the car, who has a mass of $45 \mathrm{~kg}$, moves forward a distance of $55 \mathrm{~cm}$ while being brought to rest by an inflated air bag. Assuming that the force that stops the passenger is constant, what is the magnitude of force acting on the passenger?

Prabhu Ramji

Numerade Educator

Problem 95

Medical During a front-end car collision from $48 \mathrm{~km} / \mathrm{h}$ and with air bags inflated, the acceleration limit for the chest is $60 \mathrm{~g}$ as the car comes to rest. The trunk of the body comprises about $43 \%$ of body weight. (a) For how much time does this acceleration last, assuming it is constant? (b) Draw a free-body diagram of a person during the crash. (c) What force in newtons does the air bag exert on the chest of a 72-kg person? (d) Why doesn't the force injure the person?

Linda Winkler

Numerade Educator

Problem 96

A $200-\mathrm{kg}$ block is hoisted up by two massless pulleys as shown in Figure 4-51. If a force of $1500 \mathrm{~N}$ is applied to the massless rope, what is the acceleration of the suspended mass?

Prabhu Ramji

Numerade Educator

Problem 97

A window washer sits in a bosun's chair that dangles from a massless rope that runs over a massless, frictionless pulley and back down to the man's hand. The combined mass of man, chair, and bucket is $95.0 \mathrm{~kg}$. With how much force must he pull downward to raise

Prabhu Ramji

Numerade Educator

Problem 98

A $9800-\mathrm{kg}$ alpine cable car hanging on a support cable is accelerated up a $30^{\circ}$ incline at $0.78 \mathrm{~m} / \mathrm{s}^{2}$ by a second cable attached to a support tower. Assuming the cables are straight, what is the difference in tension between the section of cable above the car and the section below the car?

Ashwin Banarsee

Ashwin Banarsee

Numerade Educator

Problem 99

Two blocks are in contact on a horizontal, frictionless surface. Block 1 has a mass of $1.0 \mathrm{~kg}$ and block 2 has a mass of $0.5 \mathrm{~kg}$. If a horizontal force with a magnitude of $7.5 \mathrm{~N}$ is applied to block 1 , what is the magnitude of the force that acts on block 2?

Sachin Rao

Numerade Educator

Problem 100

Three boxes are lined up so that they are touching each other as shown in Figure 4-52. Box $\mathrm{A}$ has a mass of $20 \mathrm{~kg}$, box $B$ has a mass of $30 \mathrm{~kg}$, and box $C$ has a mass of $50 \mathrm{~kg}$. If an external force $(F)$ pushes on box $\mathrm{A}$ toward the right, and the force that box $B$ exerts on box $C$ is $200 \mathrm{~N}$, find the acceleration of the boxes and the value of the external force $F$.

Prabhu Ramji

Numerade Educator

Problem 101

Two blocks connected by a light string are being pulled across a frictionless horizontal tabletop by a hanging 10- $\mathrm{N}$ weight (block C) (Figure 4-53). Block A has a mass of $2 \mathrm{~kg}$. The mass of block $B$ is only $1 \mathrm{~kg}$. The blocks gain speed as they move toward the right, and the strings remain taut at all times. What are the values of the tensions $T_{1}$ and $T_{2}$ ? SSM

Prabhu Ramji

Numerade Educator

Problem 102

A 2-kg object is connected with a massless string across a massless, frictionless pulley to a $3-\mathrm{kg}$ object (Figure 4-54). The smaller object rests on an inclined plane which is tilted at $40^{\circ}$ as shown. Find the acceleration of the system and the tension in the string.

Prabhu Ramji

Numerade Educator

Problem 103

A 1-kg object is connected with a string to a $2-\mathrm{kg}$ object, which is connected with a second string over a massless, frictionless pulley to a 4-kg object (Figure 4-55). The 2-kg object is connected with a second string over a massless, frictionless pulley to a 4-kg object as shown. Find the acceleration of the system and the tension in both strings. Assume the strings have negligible mass and do not stretch, and assume the level tabletop is frictionless.

Prabhu Ramji

Numerade Educator

Problem 104

A $1-\mathrm{kg}$ object is connected with a string to a 2-kg object, which is connected with a second string over a massless, frictionless pulley to a 4-kg object (Figure 4-56). The first two objects are placed onto a frictionless inclined plane. Find the acceleration of the masses and the tensions in both strings.

Prabhu Ramji

Numerade Educator

Problem 105

A $1-\mathrm{kg}$ object is connected with a string to a 2-kg object, which is connected with a second string over a massless, frictionless pulley to a 4-kg object (Figure 4-56). The first two objects are placed onto a frictionless inclined plane. Find the acceleration of the masses and the tensions in both strings.

Prabhu Ramji

Numerade Educator

Problem 106

Medical, Astro The space shuttle takes off vertically from rest with an acceleration of $29 \mathrm{~m} / \mathrm{s}^{2}$. What force is exerted on a $75-\mathrm{kg}$ astronaut during takeoff? Express your answer in newtons and also as a multiple of the astronaut's weight on Earth.

Prabhu Ramji

Numerade Educator

Problem 107

A bulldozer pushes a mound of dirt with a constant force of $3500 \mathrm{~N}$ and at a constant speed of $4 \mathrm{~m} / \mathrm{s}$. At what rate does the dirt "build up" in front of the blade of the bulldozer?

Sanjeev Kumar

Numerade Educator

Problem 108

Sports An athlete drops from rest from a platform $10 \mathrm{~m}$ above the surface of a 5 -m-deep pool. Assuming that the athlete enters the water vertically and moves through the water with constant acceleration, what is the minimum average force the water must exert on a $62-\mathrm{kg}$ diver to prevent her from hitting the bottom of the pool? Express your answer in newtons and also as a multiple of the diver's weight.

Supratim Pal

Numerade Educator

Problem 109

A person pulls three crates over a smooth horizontal floor as shown in Figure 4-58. The crates are connected to each other by identical horizontal strings $A$ and $B$, each of which can support a maximum tension of $45.0 \mathrm{~N}$ before breaking. (a) What is the largest force that can be exerted without breaking either of the strings? (b) What are the tensions in A and B just before when string breaks?

Linda Winkler

Numerade Educator

Problem 110

A 275-g hard rubber ball falls from a height of $2.20 \mathrm{~m}$. After each bounce, it rebounds to $75.0 \%$ of its previous height. High-speed photos reveal that the ball is in contact with the floor for $18.4 \mathrm{~ms}$ during each bounce. (a) Draw a free-body diagram of the ball before it hits the floor, (b) while it is in contact with the floor, and (c) after it has bounced and is rising. (d) What average force (magnitude and direction) does the floor exert on the ball during the first bounce?

Khoobchandra Agrawal

Khoobchandra Agrawal

Numerade Educator

Problem 111

'The mass of an object changes with time according to $m(t)=m_{0} e^{-b t}$, where $m_{0}$ is the initial mass and $b$ is a proportionality constant with units of $s^{-1}$. The velocity of the object also changes with time, according to $v(t)=a t+v_{0}$, where $v_{0}$ is the initial velocity and $a$ is the object's constant acceleration. (a) Determine an expression for the force on the object at any time $t$. (b) Determine the force when $m_{0}=2 \mathrm{~kg}, b=0.16 \mathrm{~s}^{-1}$, $v_{0}=1 \mathrm{~m} / \mathrm{s}, a=6 \mathrm{~m} / \mathrm{s}^{2}$, and $t=3 \mathrm{~s}$.

Surjit Tewari

Numerade Educator