• Home
  • Textbooks
  • Physics for Scientist and Engineers: A Strategic Approach
  • Dynamics I: Motion Along a Line

Physics for Scientist and Engineers: A Strategic Approach

Randall Knight

Chapter 6

Dynamics I: Motion Along a Line - all with Video Answers

Educators

Chapter Questions

04:15

Problem 1

The three ropes in Figures Ex 6.1 are tied to a small, very light ring. Two of the ropes are anchored to walls at right angles, and the third rope pulls as shown. What are $T_{1}$ and $T_{2},$ the magnitudes of the tension forces in the first two ropes? (FIGURES CAN'T COPY)

Meghan Miholics
Meghan Miholics
Numerade Educator
04:41

Problem 2

The three ropes in Figures Ex 6.2 are tied to a small, very light ring. Two of these ropes are anchored to walls at right angles with the tensions shown in the figure. What are the magnitude and direction of the tension $\vec{T}_{3}$ in the third rope?

Meghan Miholics
Meghan Miholics
Numerade Educator
06:15

Problem 3

A $20 \mathrm{kg}$ loudspeaker is suspended $2.0 \mathrm{m}$ below the ceiling by two 3.0 -m-long cables that angle outward at equal angles. What is the tension in the cables?

Meghan Miholics
Meghan Miholics
Numerade Educator
04:43

Problem 4

A football coach sits on a sled while two of his players build their strength by dragging the sled across the field with ropes. The friction force on the sled is $1000 \mathrm{N}$ and the angle between the two ropes is $20^{\circ} .$ How hard must each player pull to drag the coach at a steady $2.0 \mathrm{m} / \mathrm{s} ?$

Meghan Miholics
Meghan Miholics
Numerade Educator
05:36

Problem 5

In each of the two free-body diagrams, the forces are acting on a $2.0 \mathrm{kg}$ object. For each diagram, find the values of $a_{x}$ and $a_{y}$ the $x$ -and $y$ -components of the acceleration. (FIGURE CAN'T COPY)

Meghan Miholics
Meghan Miholics
Numerade Educator
09:45

Problem 6

In each of the two free-body diagrams, the forces are acting on a $2.0 \mathrm{kg}$ object. For each diagram, find the values of $a_{x}$ and $a_{y}$ the $x$ - and $y$ -components of the acceleration. (FIGURE CAN'T COPY)

Meghan Miholics
Meghan Miholics
Numerade Educator
08:22

Problem 7

In each of the two free-body diagrams, the forces are acting on a $5.0 \mathrm{kg}$ object. For each diagram, find the values of $a_{x}$ and $a_{y}$ the $x$ - and $y$ -components of the acceleration. (FIGURE CAN'T COPY)

Meghan Miholics
Meghan Miholics
Numerade Educator
02:46

Problem 8

Shows the velocity graph of a $2.0 \mathrm{kg}$ object as it moves along the $x$ -axis. What is the net force acting on this object at $t=1$ s? At 4 s? At 7 s? (FIGURE CAN'T COPY)

Sachin Rao
Sachin Rao
Numerade Educator
05:33

Problem 9

Shows the force acting on a $2.0 \mathrm{kg}$ object as it moves along the $x$ -axis. The object is at rest at the origin at $t=0$ s. What are its acceleration and velocity at $t=6 \mathrm{s} ?$

Meghan Miholics
Meghan Miholics
Numerade Educator
04:38

Problem 10

A horizontal rope is tied to a $50 \mathrm{kg}$ box on frictionless ice. What is the tension in the rope if:
a. The box is at rest?
b. The box moves at a steady $5.0 \mathrm{m} / \mathrm{s} ?$
c. The box has $v_{x}=5.0 \mathrm{m} / \mathrm{s}$ and $a_{x}=5.0 \mathrm{m} / \mathrm{s}^{2} ?$

Meghan Miholics
Meghan Miholics
Numerade Educator
07:22

Problem 11

A $50 \mathrm{kg}$ box hangs from a rope. What is the tension in the rope if:
a. The box is at rest?
b. The box moves up at a steady $5.0 \mathrm{m} / \mathrm{s} ?$
c. The box has $v_{y}=5.0 \mathrm{m} / \mathrm{s}$ and is speeding up at $5.0 \mathrm{m} / \mathrm{s}^{2} ?$
d. The box has $v_{y}=5.0 \mathrm{m} / \mathrm{s}$ and is slowing down at $5.0 \mathrm{m} / \mathrm{s}^{2} ?$

Meghan Miholics
Meghan Miholics
Numerade Educator
03:54

Problem 12

What thrust does a $200 \mathrm{g}$ model rocket need in order to have a vertical acceleration of $10 \mathrm{m} / \mathrm{s}^{2}$
a. On Earth?
b. On the moon, where $g=1.62 \mathrm{m} / \mathrm{s}^{2} ?$

Meghan Miholics
Meghan Miholics
Numerade Educator
02:52

Problem 13

An astronaut's weight while standing on earth is $800 \mathrm{N}$. What is his weight on Mars, where $g=3.76 \mathrm{m} / \mathrm{s}^{2} ?$

Meghan Miholics
Meghan Miholics
Numerade Educator
02:29

Problem 14

A woman has a mass of 55 kg.
a. What is her weight while standing on earth?
b. What are her mass and her weight on the moon, where $g=1.62 \mathrm{m} / \mathrm{s}^{2} ?$

Meghan Miholics
Meghan Miholics
Numerade Educator
06:39

Problem 15

It takes the elevator in a skyscraper $4.0 \mathrm{s}$ to reach its cruising speed of $10 \mathrm{m} / \mathrm{s} .$ A $60 \mathrm{kg}$ passenger gets aboard on the ground floor. What is the passenger's weight
a. Before the elevator starts moving?
b. While the elevator is speeding up?
c. After the elevator reaches its cruising speed?

Meghan Miholics
Meghan Miholics
Numerade Educator
07:25

Problem 16

Shows the velocity graph of a 75 kg passenger in an elevator. What is the passenger's weight at $t=$ 1 s? At 5 s? At 9 s? (FIGURE CAN'T COPY)

Meghan Miholics
Meghan Miholics
Numerade Educator
05:07

Problem 17

Bonnie and Clyde are sliding a $300 \mathrm{kg}$ bank safe across the floor to their getaway car. The safe slides with a constant speed if Clyde pushes from behind with $385 \mathrm{N}$ of force while Bonnie pulls forward on a rope with $350 \mathrm{N}$ of force. What is the safe's coefficient of kinetic friction on the bank floor?

Meghan Miholics
Meghan Miholics
Numerade Educator
04:52

Problem 18

$A$ stubborn, $120 \mathrm{kg}$ mule sits down and refuses to move. To drag the mule to the barn, the exasperated farmer ties a rope around the mule and pulls with his maximum force of $800 \mathrm{N}$. The coefficients of friction between the mule and the ground are $\mu_{1}=0.8$ and $\mu_{1}=0.5 .$ Is the farmer able to move the mule?

Meghan Miholics
Meghan Miholics
Numerade Educator
05:02

Problem 19

A $10 \mathrm{kg}$ crate is placed on a horizontal conveyor belt. The materials are such that $\mu_{\varepsilon}=0.5$ and $\mu_{k}=0.3$
a. Draw a free-body diagram showing all the forces on the crate if the conveyer belt runs at constant speed.
b. Draw a free-body diagram showing all the forces on the crate if the conveyer belt is speeding up.
c. What is the maximum acceleration the belt can have without the crate slipping?

Meghan Miholics
Meghan Miholics
Numerade Educator
04:04

Problem 20

A $4000 \mathrm{kg}$ truck is parked on a $15^{\circ}$ slope. How big is the friction force on the truck?

Meghan Miholics
Meghan Miholics
Numerade Educator
05:29

Problem 21

A $1500 \mathrm{kg}$ car skids to a halt on a wet road where $\mu_{\mathrm{x}}=0.50$ How fast was the car traveling if it leaves $65-$ m-long skid marks?

Meghan Miholics
Meghan Miholics
Numerade Educator
04:25

Problem 22

An Airbus A320 jetliner has a takeoff mass of 75,000 kg. It reaches its takeoff speed of $82 \mathrm{m} / \mathrm{s}(180 \mathrm{mph})$ in $35 \mathrm{s}$. What is the thrust of the engines? You can neglect air resistance but not rolling friction.

Meghan Miholics
Meghan Miholics
Numerade Educator
04:05

Problem 23

A 50,000 kg locomotive is traveling at $10 \mathrm{m} / \mathrm{s}$ when its engine and brakes both fail. How far will the locomotive roll before it comes to a stop?

Vishal Gupta
Vishal Gupta
Numerade Educator
05:49

Problem 24

Estimate the size of the friction force on a baseball player sliding into second base.

Meghan Miholics
Meghan Miholics
Numerade Educator
01:33

Problem 25

A 75 kg skydiver can be modeled as a rectangular "box" with dimensions $20 \mathrm{cm} \times 40 \mathrm{cm} \times 180 \mathrm{cm} .$ What is his terminal speed if he falls feet first?

Vipender Yadav
Vipender Yadav
Numerade Educator
02:27

Problem 26

A 6.5 -cm-diameter tennis ball has a terminal speed of $26 \mathrm{m} / \mathrm{s}$ What is the ball's mass?

Meghan Miholics
Meghan Miholics
Numerade Educator
03:30

Problem 27

A $5.0 \mathrm{kg}$ object initially at rest at the origin is subjected to the time-varying force shown in nouner ps.ar. What is the object's velocity at $t=6 \mathrm{s} ?$ (FIGURE CAN'T COPY)

Meghan Miholics
Meghan Miholics
Numerade Educator
03:30

Problem 28

A $2.0 \mathrm{kg}$ object initially at rest at the origin is subjected to the time-varying force shown in FiGURE P6.28. What is the object's velocity at $t=4 \mathrm{s} ?$

Meghan Miholics
Meghan Miholics
Numerade Educator
06:45

Problem 29

A $1000 \mathrm{kg}$ steel beam is supported by two ropes. What is the tension in each? (FIGURE CAN'T COPY)

Meghan Miholics
Meghan Miholics
Numerade Educator
04:47

Problem 30

In an electricity experiment, a $1.0 \mathrm{~g}$ plastic ball is suspended on a 60 -cm-long string and given an electric charge. A charged rod brought near the ball exerts a horizontal electrical force $\vec{F}_{\text {elec }}$ on it, causing the ball to swing out to a $20^{\circ}$ angle and remain there.
a. What is the magnitude of $\vec{F}_{\text {elec }} ?$
b. What is the tension in the string?

Meghan Miholics
Meghan Miholics
Numerade Educator
06:17

Problem 31

A 500 kg piano is being lowered into position by a crane while two people steady it with ropes pulling to the sides. Bob's rope pulls to the left, $15^{\circ}$ below horizontal, with $500 \mathrm{N}$ of tension. Ellen's rope pulls toward the right, $25^{\circ}$ below horizontal.
a. What tension must Ellen maintain in her rope to keep the piano descending at a steady speed?
b. What is the tension in the main cable supporting the piano?

Meghan Miholics
Meghan Miholics
Numerade Educator
11:35

Problem 32

Henry gets into an elevator on the 50th floor of a building and it begins moving at $t=0 \mathrm{s}$ The figure shows his weight over the next 12 s.
a. Is the elevator's initial direction up or down? Explain how you can tell.
b. What is Henry's mass?
c. How far has Henry traveled at $t=12$ s?
(FIGURE CAN'T COPY)

Meghan Miholics
Meghan Miholics
Numerade Educator
04:07

Problem 33

Zach, whose mass is $80 \mathrm{kg}$, is in an elevator descending at $10 \mathrm{m} / \mathrm{s} .$ The elevator takes $3.0 \mathrm{s}$ to brake to a stop at the first floor.
a. What is Zach's weight before the elevator starts braking?
b. What is Zach's weight while the elevator is braking?

Meghan Miholics
Meghan Miholics
Numerade Educator
05:15

Problem 34

You've always wondered about the acceleration of the elevators in the 101 -story-tall Empire State Building. One day, while visiting New York, you take your bathroom scale into the elevator and stand on it. The scale reads 150 lb as the door closes. The reading varies between 120 lb and 170 1 b as the elevator travels. 101 floors. What conclusions can you draw?

Meghan Miholics
Meghan Miholics
Numerade Educator
07:18

Problem 35

An accident victim with a broken leg is being placed in traction. The patient wears a special boot with a pulley attached to the sole. The foot and boot together have a mass of $4.0 \mathrm{kg}$ and the doctor has decided to hang a $6.0 \mathrm{kg}$ mass from the rope. The boot is held suspended by the ropes and does not touch the bed.
a. Determine the amount of tension in the rope by using Newton's laws to analyze the hanging mass.
b. The net traction force needs to pull straight out on the leg. What is the proper angle $\theta$ for the upper rope?
c. What is the net traction force pulling on the leg? Hint: If the pulleys are friction less, which we will assume, the tension in the rope is constant from one end to the other. (FIGURE CAN'T COPY)

Meghan Miholics
Meghan Miholics
Numerade Educator
06:11

Problem 36

Seat belts and air bags save lives by reducing the forces exerted on the driver and passengers in an automobile collision. Cars are designed with a "crumple zone" in the front of the car. In the event of an impact, the passenger compartment decelerates over a distance of about $1 \mathrm{~m}$ as the front of the car crumples. An occupant restrained by seat belts and air bags decelerates with the car. By contrast, an unrestrained occupant keeps moving forward with no loss of speed (Newton's first law!) until hitting the dashboard or windshield. These are unyielding surfaces, and the unfortunate occupant then decelerates over a distance of only about $5 \mathrm{~mm}$
a. $A 60 \mathrm{~kg}$ person is in a head-on collision. The car's speed at impact is $15 \mathrm{~m} / \mathrm{s}$. Estimate the net force on the person if he or she is wearing a seat belt and if the air bag deploys.
b. Estimate the net force that ultimately stops the person if he or she is not restrained by a seat belt or air bag.
c. How do these two forces compare to the person's weight?

Meghan Miholics
Meghan Miholics
Numerade Educator
06:22

Problem 37

Compressed air is used to fire a $50 \mathrm{g}$ ball vertically upward from a $1.0-\mathrm{m}$ -tall tube. The air exerts an upward force of $2.0 \mathrm{N}$ on the ball as long as it is in the tube. How high does the ball go above the top of the tube?

Meghan Miholics
Meghan Miholics
Numerade Educator
08:42

Problem 38

A rifle with a barrel length of $60 \mathrm{cm}$ fires a $10 \mathrm{g}$ bullet with a horizontal speed of $400 \mathrm{m} / \mathrm{s}$. The bullet strikes a block of wood and penetrates to a depth of $12 \mathrm{cm} .$
a. What resistive force (assumed to be constant) does the wood exert on the bullet?
b. How long does it take the bullet to come to rest?
c. Draw a velocity-versus-time graph for the bullet in the wood.

Meghan Miholics
Meghan Miholics
Numerade Educator
04:23

Problem 39

$A$ 20,000 kg rocket has a rocket motor that generates $3.0 \times 10^{5} \mathrm{N}$ of thrust.
a. What is the rocket's initial upward acceleration?
b. At an altitude of 5000 m the rocket's acceleration has increased to $6.0 \mathrm{m} / \mathrm{s}^{2} .$ What mass of fuel has it burned?

Meghan Miholics
Meghan Miholics
Numerade Educator
07:13

Problem 40

A $2.0 \mathrm{kg}$ steel block is at rest on a steel table. A horizontal string pulls on the block.
a. What is the minimum string tension needed to move the block?
b. If the string tension is $20 \mathrm{N},$ what is the block's speed after moving $1.0 \mathrm{m} ?$
c. If the string tension is $20 \mathrm{N}$ and the table is coated with oil, what is the block's speed after moving $1.0 \mathrm{m} ?$

Meghan Miholics
Meghan Miholics
Numerade Educator
08:42

Problem 41

Sam, whose mass is 75 kg, takes off across level snow on his jet-powered skis. The skis have a thrust of $200 \mathrm{N}$ and a coefficient of kinetic friction on snow of $0.10 .$ Unfortunately, the skis run out of fuel after only 10 s.
a. What is Sam's top speed?
b. How far has Sam traveled when he finally coasts to a stop?

Meghan Miholics
Meghan Miholics
Numerade Educator
08:40

Problem 42

Sam, whose mass is $75 \mathrm{kg}$, takes off down a 50 -m-high, $10^{\circ}$ slope on his jet-powered skis. The skis have a thrust of $200 \mathrm{N}$. Sam's speed at the bottom is $40 \mathrm{m} / \mathrm{s}$. What is the coefficient of kinetic friction of his skis on snow?

Meghan Miholics
Meghan Miholics
Numerade Educator
04:10

Problem 43

A baggage handler drops your $10 \mathrm{kg}$ suitcase onto a conveyor belt running at $2.0 \mathrm{m} / \mathrm{s} .$ The materials are such that $\mu_{e}=0.50$ and $\mu_{k}=0.30 .$ How far is your suitcase dragged before it is riding smoothly on the belt?

Meghan Miholics
Meghan Miholics
Numerade Educator
06:09

Problem 44

You and your friend Peter are putting new shingles on a roof pitched at $25^{\circ} .$ You're sitting on the very top of the roof when Peter, who is at the edge of the roof directly below you, $5.0 \mathrm{m}$ away, asks you for the box of nails. Rather than carry the $2.5 \mathrm{kg}$ box of nails down to Peter, you decide to give the box a push and have it slide down to him. If the coefficient of kinetic friction between the box and the roof is $0.55,$ with what speed should you push the box to have it gently come to rest right at the edge of the roof?

Meghan Miholics
Meghan Miholics
Numerade Educator
06:15

Problem 45

II It's moving day, and you need to push a $100 \mathrm{~kg}$ box up a $20^{\circ}$ ramp into the truck. The coefficients of friction for the box on the ramp are $\mu_{\mathrm{s}}=0.90$ and $\mu_{\mathrm{k}}=0.60 .$ Your largest pushing force is $1000 \mathrm{~N}$. Can you get the box into the truck without assistance if you get a running start at the ramp? If you stop on the ramp, will you be able to get the box moving again?

Meghan Miholics
Meghan Miholics
Numerade Educator
02:32

Problem 46

A $2.0 \mathrm{kg}$ wood block is launched up a wooden ramp that is inclined at a $30^{\circ}$ angle. The block's initial speed is $10 \mathrm{m} / \mathrm{s}$
a. What vertical height does the block reach above its starting point?
b. What speed does it have when it slides back down to its starting point?

Supratim Pal
Supratim Pal
Numerade Educator
05:22

Problem 47

It's a snowy day and you're pulling a friend along a level road on a sled. You've both been taking physics, so she asks what you think the coefficient of friction between the sled and the snow is. You've been walking at a steady $1.5 \mathrm{m} / \mathrm{s}$, and the rope pulls up on the sled at a $30^{\circ}$ angle. You estimate that the mass of the sled, with your friend on it, is $60 \mathrm{kg}$ and that you're pulling with a force of $75 \mathrm{N}$. What answer will you give?

Meghan Miholics
Meghan Miholics
Numerade Educator
04:32

Problem 48

A horizontal rope pulls a $10 \mathrm{kg}$ wood sled across friction-less snow. A $5.0 \mathrm{kg}$ wood box rides on the sled. What is the largest tension force for which the box doesn't slip?

Meghan Miholics
Meghan Miholics
Numerade Educator
05:20

Problem 49

A pickup truck with a steel bed is carrying a steel file cabinet. If the truck's speed is $15 \mathrm{m} / \mathrm{s}$, what is shortest distance in which it can stop without the file cabinet sliding?

Meghan Miholics
Meghan Miholics
Numerade Educator
08:09

Problem 50

You're driving along at $25 \mathrm{m} / \mathrm{s}$ with your aunt's valuable antiques in the back of your pickup truck when suddenly you see a giant hole in the road 55 m ahead of you. Fortunately, your foot is right beside the brake and your reaction time is zero! Will the antiques be as fortunate?
a. Can you stop the truck before it falls into the hole?
b. If your answer to part a is yes, can you stop without the antiques sliding and being damaged? Their coefficients of friction are $\mu_{6}=0.60$ and $\mu_{x}=0.30$
Hint: You're not trying to stop in the shortest possible distance. What's your best strategy for avoiding damage to the antiques?

Meghan Miholics
Meghan Miholics
Numerade Educator
05:20

Problem 51

The $2.0 \mathrm{kg}$ wood box in FIGURES P6.51 slides down a vertical wood wall while you push on it at a $45^{\circ}$ angle. What magnitude of force should you apply to cause the box to slide down at a constant speed? (FIGURE CAN'T COPY)

Meghan Miholics
Meghan Miholics
Numerade Educator
06:24

Problem 52

A $1.0 \mathrm{kg}$ wood block is pressed against a vertical wood wall by the $12 \mathrm{N}$ force shown in FIGURES P6.52. If the block is initially at rest, will it move upward, move downward, or stay at rest?

Meghan Miholics
Meghan Miholics
Numerade Educator
05:31

Problem 53

What is the terminal speed for an 80 kg skicr going down a $40^{\circ}$ snow-covered slope on wooden skis? Assume that the skier is $1.8 \mathrm{m}$ tall and $0.40 \mathrm{m}$ wide.

Meghan Miholics
Meghan Miholics
Numerade Educator
06:06

Problem 54

A ball is shot from a compressed-air gun at twice its terminal speed.
a. What is the ball's initial acceleration, as a multiple of $g$, if it
is shot straight up?
b. What is the ball's initial acceleration, as a multiple of $g$, if it is shot straight down?
c. Draw a plausible velocity-versus-time graph for the ball that
is shot straight down.

Meghan Miholics
Meghan Miholics
Numerade Educator
09:31

Problem 55

An artist friend of yours needs help hanging a 500 lb sculpture from the ceiling. For artistic reasons, she wants to use just two ropes. One will be $30^{\circ}$ from vertical, the other $60^{\circ} .$ She needs you to determine the smallest diameter rope that can safely support this expensive piece of art. On a visit to the hardware store you find that rope is sold in increments of $\frac{1}{8}$ -inch diameter and that the safety rating is 4000 pounds per square inch of cross section. What diameter rope should you buy?

Meghan Miholics
Meghan Miholics
Numerade Educator
02:54

Problem 56

You've been called in to investigate a construction accident in which the cable broke while a crane was lifting a $4500 \mathrm{kg} \mathrm{con}$ tainer. The steel cable is $2.0 \mathrm{cm}$ in diameter and has a safety rating of $50,000 \mathrm{N}$. The crane is designed not to exceed speeds of $3.0 \mathrm{m} / \mathrm{s}$ or accelerations of $1.0 \mathrm{m} / \mathrm{s}^{2},$ and your tests find that the crane is not defective. What is your conclusion? Did the crane operator recklessly lift too heavy a load? Or was the cable defective?

Meghan Miholics
Meghan Miholics
Numerade Educator
06:21

Problem 57

You've entered a "slow ski race" where the winner is the skier who takes the longest time to go down a $15^{\circ}$ slope without ever stopping. You need to choose the best wax to apply to your skis. Red wax has a coefficient of kinetic friction $0.25,$ yellow is 0.20 green is $0.15,$ and blue is $0.10 .$ Having just finished taking physics, you realize that a wax too slippery will cause you to accelerate down the slope and lose the race. But a wax that's too sticky will cause you to stop and be disqualified. You know that a strong headwind will apply a $50 \mathrm{N}$ horizontal force against you as you ski, and you know that your mass is 75 kg. Which wax do you choose?

Meghan Miholics
Meghan Miholics
Numerade Educator
01:00

Problem 58

A $1.0 \mathrm{kg}$ ball hangs from the ceiling of a truck by a 1.0 -m-long string. The back of the truck, where you are riding with the ball, has no windows and has been completely soundproofed. The truck travels along an exceedingly smooth test track, and you feel no bumps or bounces as it moves. Your only instruments are a meter stick, a protractor, and a stopwatch.
a. The driver tells you, over a loudspeaker, that the truck is either at rest, or it is moving forward at a steady speed of $5 \mathrm{m} / \mathrm{s} .$ Can you determine which it is? If so, how? If not, why not?
b. Next, the driver tells you that the truck is either moving forward with a steady speed of $5 \mathrm{m} / \mathrm{s}$, or it is accelerating at $5 \mathrm{m} / \mathrm{s}^{2} .$ Can you determine which it is? If so, how? If not, why not?
c. Suppose the truck has been accelerating forward at $5 \mathrm{m} / \mathrm{s}^{2}$ long enough for the ball to achieve a steady position. Does the ball have an acceleration? If so, what are the magnitude and direction of the ball's acceleration?
d. Draw a free-body diagram that shows all forces acting on the ball as the truck accelerates.
e. Suppose the ball makes a $10^{\circ}$ angle with the vertical. If possible, determine the truck's velocity. If possible, determine the truck's acceleration.

Manish Jain
Manish Jain
Numerade Educator
02:10

Problem 59

Imagine hanging from a big spring scale as it moves vertically with acceleration $a_{\gamma}$ Show that Equation 6.10 is the correct expression for your weight.

Meghan Miholics
Meghan Miholics
Numerade Educator
02:39

Problem 60

A particle of mass $m$ moving along the $x$ -axis experiences the net force $F_{x}=c l,$ where $c$ is a constant. The particle has velocity $v_{\mathrm{dr}}$ at $t=0 .$ Find an algebraic expression for the particle's velocity $v_{x}$ at a later time $t$.

Meghan Miholics
Meghan Miholics
Numerade Educator
04:14

Problem 61

Astronauts in space "weigh" themselves by oscillating on a spring. Suppose the position of an oscillating $75 \mathrm{kg}$ astronaut is given by $x=(0.30 \mathrm{m}) \sin ((\pi \mathrm{rad} / \mathrm{s}) \cdot t),$ where $t$ is in $\mathrm{s}$. What force does the spring exert on the astronaut at (a) $t=1.0 \mathrm{s}$ and
(b) 1.5 s. Note that the angle of the sine function is in radians.

Meghan Miholics
Meghan Miholics
Numerade Educator
06:17

Problem 62

An object moving in a liquid experiences a linear drag force: $\vec{D}=(b v, \text { direction opposite the motion), where } b$ is a constant called the $d r a g$ coefficient. For a sphere of radius $R,$ the drag constant can be computed as $b=6 \pi \eta R,$ where $\eta$ is the viscosity of the liquid.
a. Find an algebraic expression for the terminal speed $v_{\mathrm{tem}}$ of a spherical particle of radius $R$ and mass $m$ falling through a liquid of viscosity $\eta$
b. Water at $20^{\circ} \mathrm{C}$ has viscosity $\eta=1.0 \times 10^{-3} \mathrm{Ns} / \mathrm{m}^{2} .$ Sand grains have density $2400 \mathrm{kg} / \mathrm{m}^{3} .$ Suppose a 1.0 -mm-diameter sand grain is dropped into a 50 -m-decp lake whose water is a constant $20^{\circ} \mathrm{C}$. If the sand grain reaches terminal speed almost instantly (a quite good approximation), how long will
it take the sand grain to settle to the bottom of the lake?

Meghan Miholics
Meghan Miholics
Numerade Educator
03:33

Problem 63

Show a free-body diagram. For each:
a. Write a realistic dynamics problem for which this is the correct free-body diagram. Your problem should ask a question that can be answered with a value of position or velocity (such as "How far?" or "How fast?"), and should give sufficient information to allow a solution.
b. Solve your problem!
(FIGURE CAN'T COPY)

Meghan Miholics
Meghan Miholics
Numerade Educator
04:14

Problem 64

Show a free-body diagram. For each:
a. Write a realistic dynamics problem for which this is the correct free-body diagram. Your problem should ask a question that can be answered with a value of position or velocity (such as "How far?" or "How fast?"), and should give sufficient information to allow a solution.
b. Solve your problem!
(FIGURE CAN'T COPY)

Meghan Miholics
Meghan Miholics
Numerade Educator
04:44

Problem 65

Show a free-body diagram. For each:
a. Write a realistic dynamics problem for which this is the correct free-body diagram. Your problem should ask a question that can be answered with a value of position or velocity (such as "How far?" or "How fast?"), and should give sufficient information to allow a solution.
b. Solve your problem!
(FIGURE CAN'T COPY)

Meghan Miholics
Meghan Miholics
Numerade Educator
03:12

Problem 66

You are given the dynamics equations that are used to solve a problem. For each of these, you are to
a. Write a realistic problem for which these are the correct equations.
b. Draw the free-body diagram and the pictorial representation for your problem.
c. Finish the solution of the problem.
$$\begin{aligned} &-0.80 n=(1500 \mathrm{kg}) a_{x}\\&n-(1500 \mathrm{kg})\left(9.80 \mathrm{m} / \mathrm{s}^{2}\right)=0\end{aligned}$$

Meghan Miholics
Meghan Miholics
Numerade Educator
05:18

Problem 67

You are given the dynamics equations that are used to solve a problem. For each of these, you are to
a. Write a realistic problem for which these are the correct equations.
b. Draw the free-body diagram and the pictorial representation for your problem.
c. Finish the solution of the problem.
$$\begin{array}{l}
T-0.20 n-(20 \mathrm{kg})\left(9.80 \mathrm{m} / \mathrm{s}^{2}\right) \sin 20^{\circ} \\=(20 \mathrm{kg})\left(2.0 \mathrm{m} / \mathrm{s}^{2}\right) \\n-(20 \mathrm{kg})\left(9.80 \mathrm{m} / \mathrm{s}^{2}\right) \cos 20^{\circ}=0\end{array}$$

Meghan Miholics
Meghan Miholics
Numerade Educator
03:56

Problem 68

You are given the dynamics equations that are used to solve a problem. For each of these, you are to
a. Write a realistic problem for which these are the correct equations.
b. Draw the free-body diagram and the pictorial representation for your problem.
c. Finish the solution of the problem.
$$\begin{aligned}&(100 \mathrm{N}) \cos 30^{\circ}-f_{\mathrm{k}}=(20 \mathrm{kg}) a_{\mathrm{x}}\\&n+(100 N) \sin 30^{\circ}-(20 k g)\left(9.80 m / s^{2}\right)=0\\&f_{k}=0.20 n\end{aligned}$$

Meghan Miholics
Meghan Miholics
Numerade Educator
06:44

Problem 69

Try this! Hold your right hand out with your palm perpendicular to the ground, as if you were getting ready to shake hands. You can't hold anything in your palm this way because it would fall straight down. Use your left hand to hold a small object, such as a ball or a coin, against your outstretched palm, then let go as you quickly swing your hand to the left across your body, parallel to the ground. You'll find that the object stays against your palm; it doesn't slip or fall.
a. Is the condition for keeping the object against your palm one of maintaining a certain minimum velocity $v_{\min } ?$ Or one of maintaining a certain minimum acceleration $a_{\min } ?$ Explain.
b. Suppose the object's mass is $50 \mathrm{g},$ with $\mu_{3}=0.80$ and $\mu_{\mathrm{k}}=0.40 .$ Determine either $v_{\min }$ or $a_{\mathrm{min}},$ whichever you answered in part a.

Meghan Miholics
Meghan Miholics
Numerade Educator
05:59

Problem 70

A machine has an $800 \mathrm{g}$ steel shut tle that is pulled along a square steel rail by an elastic cord. The shuttle is released when the elastic cord has $20 \mathrm{N}$ tension at a $45^{\circ}$ angle. What is the initial acceleration of the shuttle? (FIGURE CAN'T COPY)

Meghan Miholics
Meghan Miholics
Numerade Educator
08:45

Problem 71

The figure shows an accelerometer, a device for measuring the horizontal acceleration of cars and airplanes. A ball is free to roll on a parabolic track described by the equation $y=x^{2},$ where both $x$ and $y$ are in meters. A scale along the bottom is used to measure the ball's horizontal position $x$. a. Find an expression that allows you to use a measured position $x$ (in $\mathrm{m}$ ) to compute the acceleration $a_{x}$ (in $\mathrm{m} / \mathrm{s}^{2}$ ). (For example, $a_{x}=3 x$ is a possible expression.)
b. What is the acceleration if $x=20 \mathrm{cm} ?$ (FIGURE CAN'T COPY)

Meghan Miholics
Meghan Miholics
Numerade Educator
03:23

Problem 72

A testing laboratory wants to determine if a new widget can withstand large accelerations and deceleration. To find out. they glue a $5.0 \mathrm{kg}$ widget to a test stand that will drive it vertically up and down. The graph shows its acceleration during the first second, starting from rest. Identify the forces acting on the widget and draw a free-body diagram.
b. Determine the value of $n_{y}$ the $y$ -component of the normal force acting on the widget, during the first second of motion. Give your answer as a graph of $n_{y}$ versus $t$
c. Your answer to part b should show an interval of time during which $n$, is negative. How can this be? Explain what it means physically for $n_{y}$ to be negative.
d. At what time is the weight of the widget a maximum? What is the acceleration at this time?
e. Is the weight of the widget ever zero? If so, at what time does this happen? What is the acceleration at that time?
f. Suppose the technician forgets to glue the widget to the test stand. Will the widget remain on the test stand throughout the first second, or will it fly off the stand at some instant of time? If so, at what time will this occur? (FIGURE CAN'T COPY)

Anand Jangid
Anand Jangid
Numerade Educator
06:37

Problem 73

An object moving in a liquid experiences a linear drag force: $\vec{D}=(b v, \text { direction opposite the motion }),$ where $b$ is a constant called the drag coefficient. For a sphere of radius $R$, the drag constant can be computed as $b=6 \pi \eta R,$ where $\eta$ is the viscosity of the liquid.
a. Find an algebraic expression for $v_{x}(t),$ the $x$ -component of velocity as a function of time, for a spherical particle of radius $R$ and mass $m$ that is shot horizontally with initial speed $v_{0}$ through a liquid of viscosity $\eta$
b. Water at $20^{\circ} \mathrm{C}$ has viscosity $\eta=1.0 \times 10^{-3} \mathrm{Ns} / \mathrm{m}^{2} .$ Suppose a $4.0-\mathrm{cm}$ -diameter, $33 \mathrm{g}$ ball is shot horizontally into a tank of $20^{\circ} \mathrm{C}$ water. How long will it take for the horizontal speed to decrease to $50 \%$ of its initial value?

Meghan Miholics
Meghan Miholics
Numerade Educator
07:50

Problem 74

An object moving in a liquid experiences a linear drag force:
$\vec{D}=(b v, \text { direction opposite the motion }),$ where $b$ is a constant called the drag coefficient. For a sphere of radius $R,$ the drag constant can be computed as $b=6 \pi \eta R,$ where $\eta$ is the viscosity of the liquid.
a. Use what you've learned in calculus to prove that $$a_{x}=v_{x} \frac{d v_{x}}{d x}$$
b. Find an algebraic expression for $v_{2}(x),$ the $x$ -component of velocity as a function of distance traveled, for a spherical particle of radius $R$ and mass $m$ that is shot horizontally with initial speed $v_{0}$ through a liquid of viscosity $\eta$
c. Water at $20^{\circ} \mathrm{C}$ has viscosity $\eta=1.0 \times 10^{-3} \mathrm{Ns} / \mathrm{m}^{2} .$ Suppose a 1.0 -cm-diameter, $1.0 \mathrm{g}$ marble is shot horizontally into a tank of $20^{\circ} \mathrm{C}$ water at $10 \mathrm{cm} / \mathrm{s}$. How far will it travel before stopping?

Meghan Miholics
Meghan Miholics
Numerade Educator
11:06

Problem 75

An object with cross section $A$ is shot horizontally across frictionless ice. Its initial velocity is $v_{a x}$ at $t_{0}=0$ s. Air resistance is not negligible.
Show that the velocity at time $t$ is given by the expression
$$
v_{x}=\frac{v_{0 x}}{1+A v_{0 x}, 1 / 4 m}
$$
b. $\quad A 1.6-\mathrm{m}$ -wide, $1.4-\mathrm{m}-$ high $, 1500 \mathrm{~kg}$ car hits a very slick patch of ice while going $20 \mathrm{~m} / \mathrm{s}$. If friction is neglected, how long will it take until the car's speed drops to $10 \mathrm{~m} / \mathrm{s} 7$ To $5 \mathrm{~m} / \mathrm{s} ?$
c. Assess whether or not it is reasonable to neglect kinetic friction.

Meghan Miholics
Meghan Miholics
Numerade Educator