Potential Energy Mastering Physics

7/21/2019 Potential Energy Mastering Physics

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2/23

9/20/2014 POTENTIAL ENERGY

http://session.masteringphysics.com/myct/assignmentPrintView?displayMode=studentView&assignmentID=2941502 2

Correct

Item 2

A hammer of mass is moving at speed when it strikes a nail of negligible mass that is stuck in a wooden block. The hammer is observed to drive the

nail a distance deeper into the block.

Part A

Find the magnitude of the force that the wooden block exerts on the nail, assuming that this force is independent of the depth of penetration of the

nail into the wood. You may also assume that , so that the change in the hammer's gravitational potential energy, as it drives the nail int

the block, is insignificant.

Express the magnitude of the force in terms of , , and .

Hint 1. How to approach the problem

One way to solve this problem is to use the work-energy theorem. To stop the hammer from moving, the wooden block-nail system must do a

certain amount of work on the hammer. One expression for this amount of work involves and the displacement of the hammer. In addition, the

work-energy theorem implies that the initial kinetic energy of the hammer plus the work done on the hammer must equal the final kinetic energy

of the hammer. This gives another expression for the work done that involves only the change in kinetic energy of the hammer. Equate the two

expressions for the work done and solve for .

Hint 2. Find the work done in terms of

The work-energy theorem connects the work needed to stop the hammer with the change in the hammer's kinetic energy. Find the work done

onthe hammer bythe nail. Don't forget to consider the signof your answer.

Express your answer in terms of and .

ANSWER:

Hint 3. Find the change in kinetic energy of the hammer

What is , the change in kinetic energy of the hammer?


ANSWER:

ANSWER:

Correct

Part B

Now evaluate the magnitude of the holding force of the wooden block on the nail by assuming that the force necessary to pull the nail out is the same

that needed to drive it in, which we just derived. Assume a relatively heavy hammer (about 18 ounces), moving with speed

(If such a hammer were swung this hard upward and released, it would rise 5 m). Take the penetration depth to be 2 cm, which is appropriate for o

hit on a relatively heavy construction nail.

=W

2

L

2

M

0

L

F

0

2 L

M

0

L

F

F

F

W

F L

=W

KK

f i

M

0

= KKf i

=F M ( ) 02

2 L

M = 0 . 5 k g = 1 0 m /

0

L

1 l b = 4 . 4 5 N


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Express your answer to the nearest pound. (Note: .)

ANSWER:

Correct

Item 3

A block of weight sits on an inclined plane as shown. A force of magnitude is applied to pull

the block up the incline at constant speed. The coefficient of kinetic friction between the plane and

the block is .

Part A

What is the total work done on the block by the force of friction as the block moves a distance up the incline?

Express the work done by friction in terms of any or all of the variables , , , , , and .

Hint 1. How to start

Draw a free-body force diagram showing all real forces acting on the block.

Hint 2. Find the magnitude of the friction force

Write an expression for the magnitude of the friction force.

Express your answer in terms of any or all of the variables , , , and .

Hint 1. Find the magnitude of the normal force

What is the magnitude of the normal force?

Express your answer in terms of , , and .

ANSWER:

ANSWER:

ANSWER:

1 l b = 4 . 4 5 N

= 281 lb| |F

F

W

f r i c

L

L F

F

f r i c

N

=N

=Ff r i c


4/23



Correct

Part B

What is the total work done on the block by the applied force as the block moves a distance up the incline?

Express your answer in terms of any or all of the variables , , , , , and .

ANSWER:

Correct

Now the applied force is changed so that instead of pulling the block up the incline, the force pulls the block down the incline at a constant speed.

Part C

What is the total work done on the block by the force of friction as the block moves a distance down the incline?


ANSWER:

Correct

Part D

What is the total work done on the box by the appled force in this case?


ANSWER:

Correct

Item 4

=Wf r i c

( L c o s )

W

F

F

L

L F

=WF

F L

W

f r i c

L

L F

=Wf r i c

( L c o s )

W

F

L F

=WF

F L


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Six pendulums of various masses are released from various heights above a tabletop, as shown in the figures below. All the pendulums have the sa

length and are mounted such that at the vertical position their lowest points are the height of the tabletop and just do not strike the tabletop when released

Assume that the size of each bob is negligible.

Part A

Rank each pendulum on the basis of its initial gravitational potential energy (before being released) relative to the tabletop.

Rank from largest to smallest To rank items as equivalent, overlap them.

Hint 1. Gravitational potential energy

Gravitational potential energy is defined as the product of the mass of the object, the acceleration due to gravity, and the height of the object

above a reference level, summarized as

.

ANSWER:

Incorrect; correct answer withheld by instructor

Part B

Rank each pendulum on the basis of the maximum kinetic energy it attains after release.


Hint 1. Kinetic energy

Each pendulum begins at rest (i.e., kinetic energy of zero). The maximum kinetic energy for a pendulum will occur when it is at the lowest point

in its motion. At this point, all of the pendulums will be the same height above the tabletop. The kinetic energy then will equal the change in

potential energy from the initial point to the point just above the tabletop.

ANSWER:

U

U =


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Part C

Rank each pendulum on the basis of its maximum speed.


Hint 1. The role of mass

Both kinetic energy and gravitational potential energy are proportional to mass. Thus, a pendulum with larger mass has a larger potential energy

upon release, and a larger kinetic energy at its lowest point. Since the kinetic energy is equal to the change in potential energy, you may write

down the equation . Notice that mass may be canceled from both sides. Thus, the final speed depends upon the change in

height but is independent of mass.

The situation is similar to that of an object in free fall. In free fall, although larger masses are acted upon by a larger gravitational force, a larger

mass also has more inertia. These two effects cancel out. All objects fall with the same acceleration, and therefore reach the same velocity after

falling equal distances.

ANSWER:

=

1

/

2

2


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Correct

Item 5

A baseball is thrown directly upward at time and is caught again at time . Assume that air resistance is so small that it can be ignored and th

the zero point of gravitational potential energy is located at the position at which the ball leaves the thrower's hand.

Part A

Sketch a graph of the kinetic energy of the baseball.

Hint 1. Determine the sign of the initial kinetic energy

At the instant the ball leaves the thrower's hand, is its kinetic energy positive, negative, or zero?

ANSWER:

Hint 2. The shape of the kinetic energy graph

The ball's speed decreases linearly from its initial value, which we can denote by , because of the constant acceleration due to gravity. The

velocity of the ball can be described by the equation

.

Since kinetic energy depends on the square of velocity, how does the kinetic energy vary with time?

Also, note that the ball reaches its maximum height halfway between the time that it leaves the thrower's hand and the moment it is caught. What

is the speed of the ball when it reaches the maximum height?

ANSWER:

= 0 = 5 s

positive

negative

zero

0

(

) =

0


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Correct

Part B

Based on the graph of kinetic energy given (gray curve in the graphing window), sketch a graph of the baseball's gravitational potential energy.

Hint 1. Initial gravitational potential energy

The point at which the ball leaves the thrower's hand is defined to be the origin of the yaxis, and the gravitational potential energy of the ball

depends on the ball's height above the origin.

Hint 2. The shape of the gravitational potential energy graph

The potential energy of the ball is proportional to its height, and the height of the ball can be described by the equation

.

Hint 3. Using conservation of energy

Since there are no nonconservative forces acting on the ball, the total energy must remain the same throughout the motion. Therefore, your

graph of potential energy should be shaped such that potential energy plus kinetic energy does not change during the motion.

ANSWER:

( ) =

0

1

2

2


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Correct

Part C

Based on the kinetic and potential energy graphs given, sketch a graph of the baseball's total energy.

Hint 1. Total energy

The total energy of the baseball is the sum of its kinetic energy and gravitational potential energy.

ANSWER:

Correct

Item 6


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A block of weight sits on a plane inclined at an angle as shown. The coefficient of kinetic

friction between the plane and the block is .

A force is applied to push the block up the incline at constant speed.

Part A

What is the work done on the block by the force of friction as the block moves a distance up the incline?

Express your answer in terms of some or all of the following: , , , .

Hint 1.A formula for work

The work done by a constant force is given by the dot product of the force vector with the vector representing the displacement over which the

force is applied.

Hint 2. Find the magnitude of the frictional force

What is the magnitude of the frictional force?

Express your answer in terms of , , and .

Hint 1. Compute the normal force

Find the magnitude of the normal force on the block.


ANSWER:

ANSWER:

ANSWER:


Part B

What is the work done by the applied force of magnitude ?


F

W

f

L

L

f

=

=f

=Wf

( c o s L )

W F

L


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ANSWER:


Part C

What is the change in the potential energy of the block, , after it has been pushed a distance up the incline?


ANSWER:

Correct

Now the applied force is changed so that instead of pulling the block up the incline, the force pulls the block down the incline at a constant speed.

Part D

What is the change in potential energy of the block, , as it moves a distance downthe incline?


ANSWER:

Correct

Part E

What is the work done by the applied force of magnitude ?


ANSWER:

Correct

Part F

=WF L

U L

L

= U L s i n

F

U L

L

= U s i n ( ) L

W F

L

=W ( s i n ( ) c o s ( ) ) L

W

f


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What is the work done on the block by the frictional force?


ANSWER:

Correct

Item 7

Look at this applet. It shows an elevator with a small initial upward velocity being raised by a cable. The tension in the cable is constant. The energy bar

graphs are marked in intervals of 600 .

Part A

What is the mass of the elevator? Use for the magnitude of the acceleration of gravity.

Express your answer in kilograms to two significant figures.

Hint 1. Using the graphs

Think about which graph(s) show energies that are directly related to the mass of the elevator. There may be more than one. You would like to

get the most accurate number you can, so choose the graph that you can read most accurately.

Hint 2. Needed formula

Recall that the gravitational potential energy near the earth's surface is given by , where is the mass of the object, is the

magnitude of the gravitational acceleration, and is the height above the ground.

ANSWER:

Correct

Part B

Find the magnitude of the tension in the cable. Be certain that the method you are using will be accurate to two significant figures.

Express your answer in newtons to two significant figures.

Hint 1. How to approach the problem

In the previous part, you could use the graph of potential energy to determine the mass to two significant figures, because when the elevator

stopped, the top of the potential energy bar lay right on one of the grid lines. In this problem, you could use the graph of work to find the tension,

but since it lies somewhere between the grid lines, it is unlikely that you could determine the tension to the necessary accuracy. However, it is a

good way to get an estimate with which to check your answer.

The numerical data given in the window beneath the graphs do have two significant figures of accuracy, and thus they could be used in

combination with the data in the graph of the final energy to get a more accurate value for the work done on the elevator. Recall, in fact, that the

work done on the elevator by the tension must equal the change in mechanical energy of the system.

Hint 2. Find the change in mechanical energy

From the information given in the applet and the information found in Part A, determine the change in the total mechanical energy of the system

.

Express your answer in joules to two significant figures.

Hint 1. Find the initial mechanical energy

W

f

L

=Wf

L

c o s ( )

J

= 1 0 m / s

2

U U=

= 60 k g

T

E
http://session.masteringphysics.com/myct/assignmentPrintView?displayMode=studentView&assignmentID=2941502


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Assuming that the potential energy of the elevator at the instant when you run the simulation is zero, what is the initial mechanical energy

of the system?

Express your answer in joules to two significant figures.

Hint 1. Definition of mechanical energy

Recall that the mechanical energy of a system is defined as the sum of kinetic energy and potential energy,

.

Note that, at the instant when you run the simulation, the potential energy of the elevator is zero. Thus, the total initial

mechanical energy of the system is simply given by the initial kinetic energy of the elevator , which can beevaluated from the information about the mass of the elevator found in Part A, and the information about the initial speed of the

elevator given in the window beneath the bar graphs in the applet.

ANSWER:

ANSWER:

ANSWER:

Correct

Item 8

A 115 mail bag hangs by a vertical rope 4.0 long. A postal worker then displaces the bag to a position 2.2 sideways from its original position, alway

keeping the rope taut.

Part A

What horizontal force is necessary to hold the bag in the new position?

Express your answer using two significant figures.

ANSWER:

Correct

Part B

As the bag is moved to this position, how much work is done by the rope?


ANSWER:

Correct

E

i n i t i a l

E = K + U

U

K = ( 1 / 2 )

2

=Ei n i t i a l

J

= E J

= 480T N

k g m m

= 740F N

= 0W J


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Part C

As the bag is moved to this position, how much work is done by the worker?


ANSWER:


Item 9

A spring-loaded toy gun is used to shoot a ball of mass straight up in the air, as shown in the figure. The spring has spring constant

. If the spring is compressed a distance of 25.0 centimeters from its equilibrium

position and then released, the ball reaches a maximum height (measured from the

equilibrium position of the spring). There is no air resistance, and the ball never touches the inside

of the gun. Assume that all movement occurs in a straight line up and down along the yaxis.

Part A

Which of the following statements are true?

Check all that apply.

Hint 1. Nonconservative forces

Dissipative, or nonconservative, forces are those that always oppose the motion of the object on which they act. Forces such as friction and drag

are dissipative forces.

Hint 2. Forces acting on the ball

The ball is acted on by the spring force only when the two are in contact. The force of tension in the spring is a conservative force. Also, the ball

is always acted on by gravity, which is also a conservative, or nondissipative, force.

ANSWER:

Correct

Part B

Find the muzzle velocity of the ball (i.e., the velocity of the ball at the spring's equilibrium position ).

Hint 1. Determine how to approach the problem

=Ww o r k e r

0 J

= 1 . 5 0 k g

= 6 6 7 N / m

= 0

m a x

Mechanical energy is conserved because no dissipative forces perform work on the ball.

The forces of gravity and the spring have potential energies associated with them.

No conservative forces act in this problem after the ball is released from the spring gun.

m

= 0


15/23



What physical relationship can you use to solve this problem? Choose the best answer.

ANSWER:

Hint 2. Energy equations

Recall that kinetic energy is given by the equation

,

where is the speed of the object and is the object's mass.

Gravitational potential energy is given by

,

where is the object's height measured from .

The elastic potential energy of a spring is given by

,

where is the spring constant and is the spring's displacement from equilibrium.

Hint 3. Determine which two locations you should examine

Pick the two points along the ball's path that would be most useful to compare in order to find the solution to this problem. Choose from among

the following three points:


ANSWER:

Hint 4. Find the initial energy of the system

A useful statement of mechanical energy conservation relating the initial and final kinetic ( ) and potential ( ) energies is

.

In this situation, the initial position is and the final position is , which is the equilibrium position of the spring. What kind(s)

of energy does the system "spring-ball" have at the initial position?

ANSWER:

Hint 5. Determine the final energy

A useful statement of mechanical energy conservation relating the initial and final kinetic ( ) and potential ( ) energies is

.

In this situation, the initial position is and the final position is , which is the equilibrium position of the spring. What kind(s)

of energy does the system "spring-ball" have at the final position?

kinematics equations

Newton's second law

law of conservation of energy

conservation of momentum

1

2

2

= 0

1

2

2

, the location of the ball when the spring is compressed.

, the equilibrium position of the spring.

, the maximum height that the ball reaches above the point .

= 2 5 c m

= 0

=

m a x

= 0

K U

+ = +K

i n i t i a l

U

i n i t i a l

K

f i n a l

U

f i n a l

= 2 5 . 0 c m = 0

kinetic only

elastic potential only

gravitational potential only

kinetic and gravitational potential

kinetic and elastic potential

elastic and gravitational potentials

K U

+ = +K

i n i t i a l

U

i n i t i a l

K

f i n a l

U

f i n a l

= 2 5 . 0 c m = 0


16/23



ANSWER:

Hint 6. Creating an equation

From the hints you now know what kinds of energy are present at the initial and final positions chosen for the ball in this part of the problem. You

also know that

.

It has been determined that is zero and consists of two terms: gravitational potential energy and elastic potential energy. In

addition, is zero.

ANSWER:

Correct

Part C

Find the maximum height of the ball.

Express your answer numerically, in meters.

Hint 1. Choose two locations to examine

Pick the two points along the ball's movement that would be most useful to compare in order to find a solution to this problem. Choose from

among the following three points:


ANSWER:

Hint 2. Find the initial energy

A useful statement of mechanical energy conservation is

.

Recall that in the problem statement, is set to correspond to the equilibrium position of the spring. Therefore, in this situation, the initial

location is at and the final position should be taken as .

What kind(s) of energy does the ball have at the initial location?

ANSWER:

kinetic only






+ = +K

i n i t i a l

U

i n i t i a l

K

f i n a l

U

f i n a l

K

i n i t i a l

U

i n i t i a l

U

f i n a l

= 4.78m

m / s

m a x

, the location of the ball when the spring is compressed.

, the equilibrium position of the spring.

, the maximum height that the ball reaches measured from .

= 2 5 c m

= 0

=

m a x

= 0

+ = +K

i n i t a l

U

i n i t i a l

K

f i n a l

U

f i n a l

= 0

= 2 5 c m =

m a x


17/23



Hint 3. Determine the final energyA useful statement of mechanical energy conservation is

.

In this situation, the initial location is at , and the final position should be taken as . What kind(s) of energy does the ball

have at ?

Hint 1. Find the speed of the ball at the top of its trajectory

What is the speed of the ball at the top of its trajectory?

Express your answer numerically, in meters per second.

Hint 1. Motion in the vertical direction

Recall from kinematics that a ball travels upward until its speed decreases to zero, at which point it starts falling back to Earth.

ANSWER:

ANSWER:

Hint 4. Creating an equation

From the above hints, you now know what kind of energy is present at the inital and final positions chosen for the ball in this part of the problem.

You know that

.

It was determined that is zero and that consists of two terms: gravitational potential energy and elastic potential energy. Inaddition, is zero.

ANSWER:

Correct

In this problem you practiced applying the law of conservation of mechanical energy to a physical situation to find the muzzle velocity and the

maximum height reached by the ball.

kinetic only






+ = +K

i n i t i a l

U

i n i t i a l

K

f i n a l

U

f i n a l

= 2 5 c m =

m a x

=

m a x

t o p

=t o p

m / s

kinetic only






+ = +K

i n i t i a l

U

i n i t i a l

K

f i n a l

U

f i n a l

K

i n i t i a l

U

i n i t i a l

K

f i n a l

= 1.17m a x

m


18/23



Part D

Which of the following actions, if done independently, would increase the maximum height reached by the ball?


ANSWER:

Correct

Item 10

A force of 600 stretches a certain spring a distance of 0.300 .

Part A

What is the potential energy of the spring when it is stretched a distance of 0.300 ?

ANSWER:

Correct

Part B

What is its potential energy when it is compressed a distance of 4.00 ?

ANSWER:

Correct

Item 11

An object of mass is traveling on a horizontal surface. There is a coefficient of kinetic friction between the object and the surface. The object has spe

when it reaches and encounters a spring. The object compresses the spring, stops, and then recoils and travels in the opposite direction. When t

object reaches on its return trip, it stops.

Part A

Find , the spring constant.

Express in terms of , , , and .

Hint 1. Why does the object stop?

Why does the object come to rest when it returns to ?

Although more than one answer may be true of the system, you must choose the answer that explains whythe object ultimately

reducing the spring constant

increasing the spring constant

decreasing the distance the spring is compressed

increasing the distance the spring is compressed

decreasing the mass of the ball

increasing the mass of the ball

tilting the spring gun so that it is at an angle degrees from the horizontal

< 9 0

N m

m

= 90.0U1

J

c m

= 1.60U2

J

= 0

= 0

= 0


19/23



comes to a stop.

ANSWER:

Hint 2. How does friction affect the system?

Indicate which of the following statements regarding friction is/are true.


ANSWER:

Hint 3. Energy stored in a spring

The potential energy stored in a spring having constant that is compressed a distance is

.

Hint 4. Compute the compression of the spring

By what distance does the object compress the spring?

Look at the initial condition when the object originally hits the spring and the final condition when the object returns to .

Express in terms of , , and .

Hint 1. How to approach this question

Use the fact that

to solve for the distance the spring was compressed.

Hint 2. The value of

In its final position, the object is not moving. Also the spring is not compressed. Therefore .

Hint 3. Find

What is the value of ?

Express your answer in terms of some or all of the variables , , , and and , the acceleration due to gravity.

Hint 1. How to approach this part

Initially the spring is uncompressed, so the only contribution to the system's energy comes from the kinetic energy of the object.

ANSWER:

When the object reaches the second time all of its initial energy has gone into the compression and extension of the spring.

When the object reaches the second time all of its initial energy has been dissipated by friction.

is an equilibrium position and at this point the spring exerts no force on the object.

At the force of friction exactly balances the force exerted by the spring on the object.

= 0

= 0

= 0

= 0

Work done by friction is equal to , where is the mass of an object, is the magnitude of the acceleration due to gravity,

is the coefficient of kinetic friction, and is the distance the object has traveled.

Energy dissipated by friction is equal to , where is the coefficient of friction, is the acceleration due to gravity, is

the mass of the object, and is the amount of time (since encountering the spring) the object has been moving.

Friction is a conservative force.

Work done by friction is exactly equal to the negative of the energy dissipated by friction.

( 1 / 2 )

2

= F = = E

s p r i n g

0

1

2

2

= 0

= +E

f i n a l

E

i n i t i a l

W

n o n c o n s e r v a t i v e

E

f i n a l

= 0E

f i n a l

E

i n i t i a l

E

i n i t i a l

=Ei n i t i a l

W



20/23



Hint 4. Find

What is the value of ?

Express your answer in terms of some or all of the variables , , , and and , the acceleration due to gravity.


The only nonconservative force in the system is the frictional force between the object and the surface it's on. If the object moves

through a distance , the work done by friction is

ANSWER:

ANSWER:

Hint 5. Putting it all together

In the previous part, at the two ends of the motion considered, the spring had no energy, so was not part of the equation. However, you were

able to find a relation for in terms of the known quantities. To obtain an equation involving , use conservation of energy again,

,

but this time, take the initial condition to be the moment when the spring is at its maximum compression and the final condition to be the moment

when the spring returns to . So now can be written in terms of and other variables.

Hint 6. The value of

The value of is again zero.

Hint 7. Find for this part of the motion

What is the value of for this part of the motion?

Express your answer in terms of and , the spring constant, so that you end up with an equation containing .


Since the spring is at its maximum compression, the object must be momentarily at rest. So the only contribution to the energy is from the

potential energy of the spring.

ANSWER:

Hint 8. Find for this part of the motion

What is the value of for this part of the motion?

Express your answer in terms of , , , and , the acceleration due to gravity.


The only nonconservative force in the system is the frictional force between the object and the surface it's on. If the object moves through

a distance , the work done by friction is

.

W


W


W

f r i c t i o n

= = W

f r i c t i o n

=Wn o n c o n s e r v a t i v e

=

= +E

f i n a l

E

i n i t i a l

W


= 0 E

i n i t i a l

E

f i n a l

E

f i n a l

E

i n i t i a l

E

i n i t i a l

=Ei n i t i a l

W


W


W

f r i c t i o n

= = W

f r i c t i o n


21/23



ANSWER:

ANSWER:

Correct

Item 12

A 28- rock approaches the foot of a hill with a speed of 15 . This hill slopes upward at a constant angle of 40.0 above the horizontal. The coefficie

of static and kinetic friction between the hill and the rock are 0.75 and 0.20, respectively.

Part A

Use energy conservation to find the maximum height above the foot of the hill reached by the rock.


ANSWER:

Correct

Part B

Will the rock remain at rest at its highest point, or will it slide back down the hill?

ANSWER:

Correct

Part C

If the rock does slide back down, find its speed when it returns to the bottom of the hill.


ANSWER:

Correct

Item 13

A 2.8- block slides over the smooth, icy hill shown in the figure . The top of the hill is horizontal and 70 higher than its base.

=Wn o n c o n s e r v a t i v e

=8

(

2

k g m / s

= 9.3 m

remain at rest at its highest point

slide back down the hill

= 12 m / s

k g m


22/23



Part A

What minimum speed must the block have at the base of the hill so that it will not fall into the pit on the far side of the hill?


ANSWER:

Correct

Item 14

A wooden block with mass 1.60 is placed against a compressed spring at the bottom of a slope inclined at an angle of 34.0 (point ). When the spring

released, it projects the block up the incline. At point , a distance of 5.05 up the incline from , the block is moving up the incline at a speed of 6.75

and is no longer in contact with the spring. The coefficient of kinetic friction between the block and incline is = 0.45. The mass of the spring is negligible

Part A

Calculate the amount of potential energy that was initially stored in the spring.

Take free fall acceleration to be 9.80 .

ANSWER:

Correct

Item 15

A sled with rider having a combined mass of 130 travels over the perfectly smooth icy hill shown in the accompanying figure.

Part A

How far does the sled land from the foot of the cliff?

= 42

m / s

k g

A

B m A m

m / s

2

= 110U1

J

k g


23/23


ANSWER:

Correct

Item 16

Part A

Which of the following statements is/are true?


ANSWER:


Score Summary:

Your score on this assignment is 109%.

You received 21.76 out of a possible total of 20 points.

= 25.5 m

The total mechanical energy of a system, at any one instant, is either all kinetic or all potential energy.

The total mechanical energy of a system is equally divided between kinetic and potential energy.

The total mechanical energy of a system is constant only if nonconservative forces act.

The total mechanical energy of a system is constant only if conservative forces act.

Mechanical energy can be dissipated to nonmechanical forms of energy.

Potential Energy Mastering Physics

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