Mastering physics introduction to static equilibrium

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Assignment 3

Due: 11:59pm on Sunday, July 26, 2015

You will receive no credit for items you complete after the assignment is due. Grading Policy

Tactics Box 4.1 Drawing Force Vectors

Learning Goal:

To practice Tactics Box 4.1 Drawing force vectors.

To visualize how forces are exerted on objects we can use simple diagrams, such as vectors. This Tactics Box

illustrates the process of drawing a force vector by using the particle model, in which objects are treated as points.

TACTICS BOX 4.1 Drawing force vectors

1. Represent the object as a particle.

2. Place the tail of the force vector on the particle.

3. Draw the force vector as an arrow pointing in the direction that the force acts, and with a length

proportional to the size of the force.

4. Give the vector an appropriate label.

The resulting diagram for a force exerted on an object is shown in the drawing. Note that the object is represented as

a point.

Part A

A book lies on a table. A pushing force parallel to the table top and directed to the right is exerted on the book.

Use the diagram below to draw the force vector . Use the black dot as the particle representing the book and be

certain to draw the force vector so that it has the correct orientation.

Draw the vector starting from the black dot. The location and orientation of the vector will be graded. The

length of the vector will not be graded.

ANSWER:

F ⃗

F ⃗

p

F ⃗

p

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Part B

This question will be shown after you complete previous question(s).

Part C

This question will be shown after you complete previous question(s).

Problem 4.7

A mountain climber is hanging from a rope in the middle of a crevasse. The rope is vertical.

Part A

Identify the forces on the mountain climber.

Check all that apply.

ANSWER:

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Problem 4.16

A constant force is applied to an object, causing the object to accelerate at 10 .

Part A

What will the acceleration be if the force is halved?

Express your answer using two significant figures.

ANSWER:

Part B

What will the acceleration be if the object's mass is halved?

Express your answer using two significant figures.

ANSWER:

Part C

What will the acceleration be if the force and the object's mass are both halved?

Express your answer using two significant figures.

ANSWER:

Part D

What will the acceleration be if the force is halved and the object's mass is doubled?

Express your answer using two significant figures.

Kinetic friction

Weight

Static friction

Normal force

Tension

f

⃗

k

w⃗

f

⃗

s

n⃗

T

⃗

m/s

2

a = m/s

2

a = m/s

2

a = m/s

2

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ANSWER:

Problem 4.22

Two children fight over a 200 stuffed bear. The 25 boy pulls to the right with a 15 force and the 20 girl pulls

to the left with a 17 force. Ignore all other forces on the bear (such as its weight).

Part A

At this instant, can you say what the velocity of the bear is?

Enter yes or no.

ANSWER:

Part B

At this instant, can you say what the acceleration of the bear is?

Enter yes or no.

ANSWER:

Part C

This question will be shown after you complete previous question(s).

Part D

This question will be shown after you complete previous question(s).

A Book on a Table

A book weighing 5 N rests on top of a table.

a = m/s

2

g kg N kg

N

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Part A

A downward force of magnitude 5 N is exerted on the book by the force of

ANSWER:

Part B

An upward force of magnitude _____ is exerted on the _____ by the table.

ANSWER:

Part C

Do the downward force in Part A and the upward force in Part B constitute a 3rd law pair?

You did not open hints for this part.

ANSWER:

the table

gravity

inertia

.

6 N / table

5 N / table

5 N / book

6 N / book

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Part D

The reaction to the force in Part A is a force of magnitude _____, exerted on the _____ by the _____. Its direction

is _____ .

You did not open hints for this part.

ANSWER:

Part E

The reaction to the force in Part B is a force of magnitude _____, exerted on the _____ by the _____. Its direction

is _____.

ANSWER:

Part F

Which of Newton's laws could we have used to predict that the forces in Parts A and B are equal and opposite?

Check all that apply.

ANSWER:

yes

no

5 N / earth / book / upward

5 N / book / table / upward

5 N / book / earth / upward

5 N / earth / book / downward

5 N / table / book / upward

5 N / table / earth / upward

5 N / book / table / upward

5 N / table / book / downward

5 N / earth / book / downward

Newton's 1st law

Newton's 2nd law

Newton's 3rd law

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Part G

Which of Newton's laws could we have used to predict that the forces in Parts B and E are equal and opposite?

Check all that apply.

ANSWER:

PSS 5.1: Equilibrium problems

Learning Goal:

To practice Problem­Solving Strategy 5.1 Equilibrium problems

A 20­ loudspeaker is suspended 2.0 below the ceiling by two ropes that are each 30 from vertical. What is the

tension in the ropes?

PROBLEM­SOLVING STRATEGY 5.1 Equilibrium problems

PREPARE First check that the object is in equilibrium: Does ?

An object at rest is in static equilibrium.

An object moving at a constant velocity is in dynamic equilibrium.

Then identify all forces acting on the object and show them on a free­body diagram. Determine which forces are known

and which you need to solve for.

SOLVE An object in equilibrium must satisfy Newton’s second law for the case where . In component form, the

requirement is

and .

You can find the force components that go into these sums directly from your free­body diagram. From these two

Newton's 1st law

Newton's 2nd law

Newton's 3rd law

kg m ∘

a⃗= 0

⃗

a⃗= 0

⃗

∑Fx = max = 0 ∑Fy = may = 0

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equations, solve for the unknown forces in the problem.

ASSESS Check that your result has the correct units, is reasonable, and answers the question.

PREPARE

Determine what sort of equilibrium your system is in. Then, draw a free­body diagram and determine useful

relationships between the forces.

Part A

Which of the following statements are correct about the situation described in the introduction?

Check all that apply.

ANSWER:

Part B

Identify the forces acting on the loudspeaker and then draw them on the free­body diagram.

Draw the vectors starting from the black dot. The location and orientation of the vectors will be graded. The

length of the vectors will not be graded.

ANSWER:

The loudspeaker is in static equilibrium.

The loudspeaker is in dynamic equilibrium.

The loudspeaker is not in static equilibrium, because it is not on the ground.

The loudspeaker is not in dynamic equilibrium, because it is accelerating.

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Part C

This question will be shown after you complete previous question(s).

SOLVE

Use the conditions for equilibrium to determine the tensions in the two ropes.

Part D

This question will be shown after you complete previous question(s).

ASSESS

Determine whether your answer makes sense.

Part E

This question will be shown after you complete previous question(s).

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Problem 5.13

A horizontal rope is tied to a 40 box on frictionless ice.

Part A

What is the tension in the rope if the box is at rest?

Express your answer using two significant figures.

ANSWER:

Part B

What is the tension in the rope if the box moves at a steady 9.0 ?

Express your answer using two significant figures.

ANSWER:

Part C

What is the tension in the rope if the box has = 9.0 and = 5.0

Express your answer using two significant figures.

ANSWER:

Problem 5.17

A woman has a mass of 50.0 .

Part A

What is her weight on earth?

ANSWER:

kg

T = N

m/s

T = N

vx m/s ax m/s

2

T = N

kg

wearth = N

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Part B

What is her mass on the moon, where ?

ANSWER:

Part C

What is her weight on the moon, where ?

ANSWER:

Problem 5.23

Part A

A 0.57 bullfrog is sitting at rest on a level log. How large is the normal force of the log on the bullfrog?

Express your answer using two significant figures.

ANSWER:

Part B

A second 0.57 bullfrog is on a log tilted 23 above horizontal. How large is the normal force of the log on this

bullfrog?

Express your answer using two significant figures.

ANSWER:

Problem 5.25

Bonnie and Clyde are sliding 430 bank safe across the floor to their getaway car. The safe slides with a constant

speed if Clyde pushes from behind with 420 of force while Bonnie pulls forward on a rope with 260 of force.

g = 1.62 m/s

2

mmoon = kg

g = 1.62 m/s

2

wmoon = N

kg

n = N

kg

∘

n = N

kg

N N

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Part A

What is the safe's coefficient of kinetic friction on the bank floor?

ANSWER:

Score Summary:

Your score on this assignment is 0.0%.

You received 0 out of a possible total of 30 points.

μ = k

Mass (kg) Weight (N)

Acceleration (m/s2)

Scale Reading (N)

Newton's Second Law

Part A, Section B

An object with mass m = 100 kg is sitting on a scale in an elevator. Use Excel to determine the

reading on the scale (in Newtons) for the following four situations.

i) Elevator accelerating upward at 3 m/s2

ii) Elevator moving at constant speed

iii) Elevator accelerating downward at -3 m/s2

iv) Elevator accelerating downward at -9.8 m/s2

Input: Acceleration of the elevator

Output: Reading on the scale

Mass (kg)

20

40

20

20

Velocity (m/s) Force (N)

20

20

40

20

-20

-20

-40

-40

Acceleration (m/s2)

Time to come to rest (s) Stopping distance (m)

Newton's Second Law

Part B, Section A

An object with a mass m is moving with an initial speed vand is acted on by a single force F in

the opposite direction of its motion. Use Excel to determine how long it will take the object to

come to rest and how far the object travels until it stops.

i) If the mass is doubled, what is the effect on the time? On the stopping distance?

ii) If the initial velocity is doubled, what is the effect on the time? On the stopping distance?

iii) If the force is doubled, what is the effect on the time? On the stopping distance?

Input: Mass, initial velocity, force

Output: Acceleration, time to come to rest, stopping distance

Mass (kg)

Fx (N)

20,000

50,000

vx (m/s)

vy (m/s)

ay (m/s2)

100,000

time (s)

ax (m/s2)

Fy (N)

Newton's Second Law

Part B, Section B

v (m/s)

x (m)

y (m)

A rocket ship, with mass m = 20,000kg and engines mounted perpendicularly in the x- and y-directions,

fires both rockets simultaneously. The engine oriented in the x-direction fires for 3 s and shuts off. The

engine oriented in the y-direction fires for 7 s and shuts off. The force from the engine in the x-direction is

50,000 N, and the force from the engine in the y-direction is 100,000 N. Make a scatter plot of the y-position

d (m)

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

5

5.5

6

6.5

7

7.5

8

8.5

9

9.5

10

of each particle as a function of the x-position, showing the trajectory of the rocket.

Use Excel to determine the following.

i) While the engines are firing, what is the acceleration of the rocket in the x- and y-directions?

ii) After 7 s, what is the velocity of the rocket in the x- and y-directions?

iii) After 7 s, what is the speed of the rocket?

iv) After 7 s, how far has the rocket travelled in the x-direction? How far has it travelled in the y-direction?

After 10 s?

v) After 7 s, what is the displacement of the rocket? After 10 s? Is the displacement of the rocket the

same as the distance travelled? Explain.

Rocket Trajectory

y

vi) If the mass of the rocket is doubled, what happens to the displacement?

12

10

8

6

4

2

0

Output: ax, ay, vx, vy, x, y, d

0

2

4

6

x

8

10

12