linear machanics

[ Assignment View ]

HET124-Energy & Motion

Assignment 2 (Weeks 3-4)

Due at 4:00am on Monday, March 30, 2009

View Grading Details The following 5 questions (12 points) involve Newton's Laws of Motion

Motion of a Block with Three Forces

The diagram below shows a block of mass on a frictionless horizontal surface, as seen from

above. Three forces of magnitudes , , and are applied to the block, initially at rest on the surface, at angles shown on the diagram.

In this problem, you will determine the resultant (total) force vector from the combination of the three individual force vectors. All angles should be measured counterclockwise from the positive x axis (i.e., all angles are positive).

Part A

Calculate the magnitude of the total resultant force acting on the mass.

Hint A.1 Definition of resultant force

Hint not displayed

Hint A.2 How to find the resultant

Hint not displayed

Hint A.3Find the components of

Hint not displayed


Hint not displayed


Hint not displayed

Hint A.6Magnitude of

Hint not displayed

Express the magnitude of the resultant force in newtons to to two decimal places..

ANSWER: =

1.83

Part B

What angle does make with the positive x axis?

Hint B.1 Find the angle symbolically

Hint not displayed

Express your answer in degrees to two significant figures.

ANSWER:

290 degrees

Part C

What is the magnitude of the mass's acceleration vector, ?

Hint C.1 Newton's 2nd law

Hint not displayed

Express your answer to two significant figures.

ANSWER: = 0.92

Part D

What is the direction of ? In other words, what angle does this vector make with respect to the positive x axis?

Hint D.1Relation between the direction of and

Hint not displayed


ANSWER:

290 degrees

Part E

How far (in meters) will the mass move in 5.0 s?

Hint E.1 Displacement with constant acceleration

Hint not displayed

Express the distance in meters to two significant figures.

ANSWER: =

11

Part F

What is the magnitude of the velocity vector of the block at ?

Hint F.1 Velocity with constant acceleration

Hint not displayed

Express your answer in meters per second to two significant figures.

ANSWER: = 4.5

Part G

In what direction is the mass moving at time ? That is, what angle does the velocity vector make with respect to the positive x axis?

Hint G.1Relationship between the direction of and

Hint not displayed


ANSWER:

290 degrees

Pulling Two Blocks

In the situation shown in the figure, a person is pulling with a constant, nonzero force on string 1, which is attached to block A. Block A is also attached to block B via string 2, as shown.

For this problem, assume that neither string stretches and that friction is negligible. Both blocks have finite (nonzero) mass.

Part A

Which one of the following statements correctly descibes the relationship between the accelerations of blocks A and B?

Hint A.1 Relative movement of the blocks

Hint not displayed

ANSWER:

Block A has a larger acceleration than block B.

Block B has a larger acceleration than block A.

Both blocks have the same acceleration.

More information is needed to determine the relationship between the accelerations.

Since the two blocks are connected, they won't move independently when string 1 is pulled. As block A is accelerated, its motion will impart the same acceleration to block B.

Part B

How does the magnitude of the tension in string 1, , compare with the tension in string 2, ?

Hint B.1 How to approach the problem

Hint not displayed

ANSWER:

More information is needed to determine the relationship between and .

The force transmitted through string 1 (proportional to ) must be enough to accelerate both blocks, but the force transmitted through string 2 only needs to accelerate block B. Consider the case where block A is very heavy and block B is very light: In this case, string 2 would only need to supply a tiny amount of tension to keep the blocks connected as block A is pulled around.

Newton's 3rd Law Discussed

Learning Goal: To understand Newton's 3rd law, which states that a physical interaction always generates a pair of forces on the two interacting bodies.

In Principia, Newton wrote: To every action there is always opposed an equal reaction: or, the mutual actions of two bodies upon each other are always equal, and directed to contrary parts.

(translation by Cajori)

The phrase after the colon (often omitted from textbooks) makes it clear that this is a statement about the nature of force. The central idea is that physical interactions (e.g., due to gravity, bodies touching, or electric forces) cause forces to arise between pairs of bodies. Each pairwise interaction produces a pair of opposite forces, one acting on each body. In summary, each physical interaction between two bodies generates a pair of forces. Whatever the physical cause of the interaction, the force on body A from body B is equal in magnitude and opposite in direction to the force on body B from body A.

Incidentally, Newton states that the word "action" denotes both (a) the force due to an interaction and (b) the changes in momentum that it imparts to the two interacting bodies. If you haven't learned about momentum, don't worry; for now this is just a statement about the origin of forces.

Mark each of the following statements as true or false. If a statement refers to "two bodies" interacting via some force, you are not to assume that these two bodies have the same mass.

Part A

Every force has one and only one 3rd law pair force.

ANSWER:

true

false

Part B

The two forces in each pair act in opposite directions.

ANSWER:

true

false

Part C

The two forces in each pair can either both act on the same body or they can act on different bodies.

ANSWER:

true

false

Part D

The two forces in each pair may have different physical origins (for instance, one of the forces could be due to gravity, and its pair force could be due to friction or electric charge).

ANSWER:

true

false

Part E

The two forces of a 3rd law pair always act on different bodies.

ANSWER:

true

false

Part F

Given that two bodies interact via some force, the accelerations of these two bodies have the same magnitude but opposite directions. (Assume no other forces act on either body.)

Hint F.1

Hint not displayed

ANSWER:

true

false

Newton's 3rd law can be summarixed as follows: A physical interaction (e.g., gravity) operates between two interacting bodies and generates a pair of opposite forces, one on each body. It offers you a way to

test for real forces (i.e., those that belong on the force side of )--there should be a 3rd law pair force operating on some other body for each real force that acts on the body whose acceleration is under consideration.

Part G

According to Newton's 3rd law, the force on the (smaller) moon due to the (larger) earth is

ANSWER:

greater in magnitude and antiparallel to the force on the earth due to the moon.

greater in magnitude and parallel to the force on the earth due to the moon.

equal in magnitude but antiparallel to the force on the earth due to the moon.

equal in magnitude and parallel to the force on the earth due to the moon.

smaller in magnitude and antiparallel to the force on the earth due to the moon.

smaller in magnitude and parallel to the force on the earth due to the moon.

Problem 4.41

A 72 tree surgeon rides a "cherry picker" lift to reach the upper branches of a tree.

Part A

What force does the bucket of the lift exert on the surgeon when the bucket is at rest?Express your answer using two significant figures.

ANSWER: = 710

Part B

What force does the bucket of the lift exert on the surgeon when the bucket is moving upward at a steady

2.4 ?Express your answer using two significant figures.

ANSWER: = 710

Part C

What force does the bucket of the lift exert on the surgeon when the bucket is moving downward at a

steady 2.4 ?Express your answer using two significant figures.

ANSWER: = 710

Part D

What force does the bucket of the lift exert on the surgeon when the bucket is accelerating upward at

1.5 ?Express your answer using two significant figures.

ANSWER: = 810

Part E

What force does the bucket of the lift exert on the surgeon when the bucket is accelerating downward at

1.5 ?

Express your answer using two significant figures.

ANSWER: = 600

Problem 4.55

An elevator cable can withstand a maximum tension of 1.83×104 before breaking. The elevator has a

mass of 420 and a maximum acceleration of 2.27 . Engineering safety standards require that the cable tension never exceed two-thirds of the breaking tension.

Part A

How many 65.0 people can the elevator safely accommodate? Express your answer as an integer.

ANSWER: = 9

The following 8 questions (21 points) involve applications of Newton's laws.

Atwood Machine Special Cases

An Atwood machine consists of two blocks (of masses and ) tied together with a massless rope that passes over a fixed, perfect (massless and frictionless) pulley. In this problem you'll investigate some special cases where physical variables describing the Atwood machine take on limiting values. Often, examining special cases will simplify a problem, so that the solution may be found from inspection or from the results of a problem you've already seen.

For all parts of this problem, take upward to be the positive direction and take the gravitational constant, , to be positive.

Part A

Consider the case where and are both nonzero, and . Let be the magnitude of the

tension in the rope connected to the block of mass , and let be the magnitude of the tension in the rope connected to the block of mass . Which of the following statements is true?

ANSWER:

is always equal to .

is greater than by an amount independent of velocity.

is greater than but the difference decreases as the blocks increase in velocity.

There is not enough information to determine the relationship between and .

Part B

Now, consider the special case where the block of mass is not present. Find the magnitude, , of the tension in the rope. Try to do this without equations; instead, think about the physical consequences.


Hint not displayed

Hint B.2 Which physical law to use

Hint not displayed

ANSWER: = 0

Part C

For the same special case (the block of mass not present), what is the acceleration of the block of mass ?

Express your answer in terms of , and remember that an upward acceleration should be positive.

ANSWER: = -9.80

Part D

Next, consider the special case where only the block of mass is present. Find the magnitude, , of the tension in the rope.

ANSWER: = 0

Part E

For the same special case (the block of mass not present) what is the acceleration of the end of the rope where the block of mass would have been attached?Express your answer in terms of , and remember that an upward acceleration should be positive.

ANSWER: =

9.80

Part F

Next, consider the special case . What is the magnitude of the tension in the rope connecting the two blocks?Use the variable in your answer instead of or .

ANSWER: =

Part G

For the same special case ( ), what is the acceleration of the block of mass ?

ANSWER: =

0

Part H

Finally, suppose , while remains finite. What value does the the magnitude of the tension approach?

Hint H.1 Acceleration of block of mass

Hint not displayed

Hint H.2 Acceleration of block of mass

Hint not displayed

Hint H.3 Net force on block of mass

Hint not displayed

ANSWER: =

Imagining what would happen if one or more of the variables approached infinity is often a good way to investigate the behavior of a system.

Free-Body Diagrams: Introduction

Learning Goal: To learn to draw free-body diagrams for various real-life situations.

Imagine that you are given a description of a real-life situation and are asked to analyze the motion of the objects involved. Frequently, that analysis involves finding the acceleration of the objects, which, in turn, requires that you find the net force.

To find the net force, you must first identify all of the forces acting on the object and then add them as vectors. Such a procedure is not always trivial. It is helpful to replace the sketch of the situation by a drawing of the object (represented as a particle) and all the forces applied to it. Such a drawing is called a free-body diagram. This problem will walk you through several examples of free-body diagrams and will demonstrate some of the possible pitfalls.

Here is the general strategy for drawing free-body diagrams:

Identify the object of interest. This may not always be easy: A sketch of the situation may contain many objects, each of which has a different set of forces acting on it. Including forces acting on different objects in the same diagram will lead to confusion and a wrong solution.

Draw the object as a dot. Draw and clearly label all the forces acting on the object of interest. The forces should be shown as vectors originating from the dot representing the object of interest. There are two possible difficulties here: omitting some forces and drawing the forces that either don't exist at all or are applied to other objects. To avoid these two pitfalls, remember that every force must be applied to the object of interest by some other object.

Once all of the forces are drawn, draw the coordinate system. The origin should coincide with the dot representing the object of interest and the axes should be chosen so that the subsequent calculations of vector components of the forces will be relatively simple. That is, as many forces as possible must be either parallel or perpendicular to one of the axes.

Even though real life can present us with a wide variety of situations, we will be mostly dealing with a very

small number of forces. Here are the principal ones of interest:

Weight, or the force due to gravity. Weight acts on every object and is directed straight down unless we are considering a problem involving the nonflat earth (e.g., satellites).

Normal force. The normal force exists between two surfaces that are pressed against each other; it is always perpendicular to the surfaces.

Force of tension. Tension exists in strings, springs, and other objects of finite length. It is directed along the string or a spring. Keep in mind that a spring can be either compressed or stretched whereas a string can only be stretched.

Force of friction. A friction force exists between two surfaces that either move or have a tendency to move relative to each other. Sometimes, the force of air drag, similar in some ways to the force of friction, may come into play. These forces are directed so that they resist the relative motion of the surfaces. To simplify problems you often assume that friction is negligible on smooth surfaces and can be ignored. In addition, the word friction commonly refers to resistive forces other than air drag that are caused by contact between surfaces, so you can ignore air drag in problems unless you are explicitly told to consider its effects.

The following examples should help you learn to draw free-body diagrams. We will start with relatively simple situations in which the object of interest is either explicitly suggested or fairly obvious.

Part A

A hockey puck slides along a horizontal, smooth icy surface at a constant velocity as shown.

Which of the following forces act on the puck? Check all that apply.

ANSWER:

friction

weight

normal force

air drag

acceleration

force of push

force of velocity

There is no such thing as "the force of velocity." If the puck is not being pushed, there are no horizontal forces acting on it. Of course, some horizontal force must have acted on it before, to impart the velocity--however, in the situation described, no such "force of push" exists. Also, the air drag in such cases is

assumed to be negligible. Finally, the word "smooth" usually implies negligible surface friction. Your free-body diagram should look like the one shown here.

Part B

Consider a block pulled by a horizontal rope along a horizontal surface at a constant velocity as shown.

There is tension in the rope. Which of the following forces act on the block? Check all that apply.

ANSWER:

friction

weight

normal force

force of velocity

air drag

acceleration

force of tension

Because the velocity is constant, there must be a force of friction opposing the force of tension. Since the block is moving, it is kinetic friction. Your free-body diagram should look like that shown here.

Part C

A block is resting on an slope. Which of the following forces act on the block? Check all that apply.

ANSWER:

static friction

force of push

normal force

kinetic friction

weight

Part D

Draw the free-body diagram for the block resting on a slope.Draw the force vectors such that their tails align with the center of the block (indicated by the black dot). The orientations of your vectors will be graded but not the lengths.

ANSWER:

View

SUM_vec%253D0

Part E

Now consider a block sliding up a rough slope after having been given a quick push as shown

. Which of the following forces act on the block? Check all that apply.

ANSWER:

weight

kinetic friction

static friction

force of push

normal force

the force of velocity

The word "rough" implies the presence of friction. Since the block is in motion, it is kinetic friction. Once again, there is no such thing as "the force of velocity." However, it seems a tempting choice to some students since the block is going up.

Part F

Draw the free-body diagram for the block sliding up a rough slope after having been given a quick push.Draw the force vectors such that their tails align with the center of the block (indicated by the black dot). The orientations of your vectors will be graded but not the lengths.

ANSWER:

View

Part G

Now consider a block being pushed up a smooth slope. The force pushing the block is parallel to the

SUM_vec%253D0

slope. Which of the following forces are acting on the block? Check all that apply.

ANSWER:

weight

kinetic friction

static friction

force of push

normal force

Your free-body diagram should look like the one shown here.

The force of push is the normal force exerted, possibly, by the palm of the hand of the person pushing the block.

In all the previous situations just described, the object of interest was explicitly given. In the remaining parts of the problem, consider a situation where choosing the objects for which to draw the free-body diagrams is up to you.

Two blocks of masses and are connected by a light string that goes over a light frictionless pulley. The block of mass is sliding to the right on a rough horizontal surface of a lab table.

Part H

To solve for the acceleration of the blocks, you will have to draw the free-body diagrams for which objects? Check all that apply.

ANSWER:

the block of mass

the block of mass

the connecting string

the pulley

the table

the earth

Part I

Draw the free-body diagram for the block of mass and draw a free-body diagram for the block of mass .

Draw the force vectors acting on such that their tails align with the center of the block labeled (indicated by the black dot). Draw the force vectors acting on with their tails aligned with the

center of the block labeled . The orientations of your vectors will be graded but not the lengths.

ANSWER:

View

Friction Force on a Dancer on a Drawbridge

SUM_vec%253D0

A dancer is standing on one leg on a drawbridge that is about to open. The coefficients of static and kinetic

friction between the drawbridge and the dancer's foot are and , respectively. represents the normal

force exerted on the dancer by the bridge, and represents the gravitational force exerted on the dancer, as

shown in the drawing . For all the questions, we can assume that the bridge is a perfectly flat surface and lacks the curvature characteristic of most bridges.

Part A

Before the drawbridge starts to open, it is perfectly level with the ground. The dancer is standing still on

one leg. What is the x component of the friction force, ?

Hint A.1 What forces are acting?

Hint not displayed

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

ANSWER: =

0

This shows a very important point. When you are not told that an object is slipping or on the verge of slipping, then the friction force is determined using Newton's laws of motion in conjunction with the observed motion and the other forces on the object. Under these circumstances the friction force is limited by or but is otherwise not necessarily related to or .

Part B

The drawbridge then starts to rise and the dancer continues to stand on one leg. The drawbridge stops just at the point where the dancer is on the

verge of slipping. What is the magnitude of the frictional force now?

Hint B.1 Calculating the coefficient of static friction

Hint not displayed

Express your answer in terms of some or all of the variables , , and/or . The angle should not appear in your answer.

ANSWER: =

Part C

Then, because the bridge is old and poorly designed, it falls a little bit and then jerks. This causes the

person to start to slide down the bridge at a constant speed. What is the magnitude of the frictional force now?

Express your answer in terms of some or all of the variables , , and/or . The angle should not appear in your answer.

ANSWER: =

Part D

The bridge starts to come back down again. The dancer stops sliding. However, again because of the age and design of the bridge it never makes it all the way down; rather it stops half a meter short. This half a

meter corresponds to an angle degree (see the diagram, which has the angle exaggerated). What is

the force of friction now?

Hint D.1 Analyze gravitational components

Hint not displayed

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

ANSWER: =

Suspending a Speaker

A loudspeaker of mass 23.0 is suspended a distance of = 1.00 below the ceiling by two cables that

make equal angles with the ceiling. Each cable has a length of = 3.10 .

Part A

What is the tension in each of the cables?

Hint A.1 How to approach the problem

Hint not displayed

Hint A.2 Identify the forces

Hint not displayed

Hint A.3 Find the net vertical force

Hint not displayed

Hint A.4Determine

Hint not displayed

Use 9.80 for the magnitude of the acceleration due to gravity.

ANSWER: = 349

Block on an Incline Adjacent to a Wall

A wedge with an inclination of angle rests next to a wall. A block of mass is sliding down the plane, as shown. There is no friction between the wedge and the block or between the wedge and the horizontal

surface.

Part A

Find the magnitude, , of the sum of all forces acting on the block.

Hint A.1 Direction of the net force on the block

Hint not displayed

Hint A.2 Determine the forces acting on the block

Hint not displayed

Hint A.3 Find the magnitude of the force acting along the direction of motion

Hint not displayed

Express in terms of and , along with any necessary constants.

ANSWER: =

Part B

Find the magnitude, , of the force that the wall exerts on the wedge.

Hint B.1 The force between the wall and the wedge

Hint not displayed

Hint B.2 Find the normal force between the block and the wedge

Hint not displayed

Hint B.3 Find the horizontal component of the normal force

Hint not displayed

Express in terms of and , along with any necessary constants.

ANSWER: =

Your answer to Part B could be expressed as either or . In either form,

we see that as gets very small or as approaches 90 degrees ( radians), the contact force between

the wall and the wedge goes to zero. This is what we should expect; in the first limit ( small), the block

is accelerating very slowly, and all horizontal forces are small. In the second limit ( about 90 degrees), the block simply falls vertically and exerts no horizontal force on the wedge.

Problem 5.17

A tow truck is connected to a 1400 car by a cable that makes a 27 angle to the horizontal.

Part A

If the truck accelerates at 0.57 , what is the magnitude of the cable tension? Neglect friction and the mass of the cable. Express your answer using two significant figures.

ANSWER: = 900

Problem 5.29

A hockey puck is given an initial speed of 13 .

Part A

If it comes to rest in 56 , what is the coefficient of kinetic friction? Express your answer using two significant figures.

ANSWER: = 0.15

Problem 5.50

In a typical front-wheel-drive car, 70% of the car's weight rides on the front wheels.

Part A

If the coefficient of friction between tires and road is 0.61, what is the maximum acceleration of the car? Express your answer using two significant figures.

ANSWER: = 4.2

The following 6 questions (14 points) involve work and kinetic energy.

Work on a Sliding Block

A block of weight sits on a frictionless inclined plane, which makes an angle with respect to the

horizontal, as shown. A force of magnitude , applied parallel to the incline, pulls the block up the plane at constant speed.

Part A

The block moves a distance up the incline. The block does not stop after moving this distance but

continues to move with constant speed. What is the total work done on the block by all forces? (Include only the work done after the block has started moving, not the work needed to start the block moving from rest.)

Hint A.1 What physical principle to use

Hint not displayed

Hint A.2 Find the change in kinetic energy

Hint not displayed

Express your answer in terms of given quantities.

ANSWER: = 0

Part B

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

Hint B.1 Force diagram

Hint not displayed

Hint B.2 Force of gravity component

Hint not displayed

Express the work done by gravity in terms of the weight and any other quantities given in the problem introduction.

ANSWER:

=

Part C

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

Hint C.1 How to find the work done by a constant force

Hint not displayed

Express your answer in terms of and other given quantities.

ANSWER: =

Part D

What is , the work done on the block by the normal force as the block moves a distance up the inclined plane?

Hint D.1 First step in computing the work

Hint not displayed

Express your answer in terms of given quantities.

ANSWER: = 0

Dragging a Board

A uniform board of length and mass lies near a boundary that separates two regions. In region 1, the coefficient of kinetic friction between the board and the surface is , and in region 2, the coefficient is . The positive direction is shown in the figure.

Part A

Find the net work done by friction in pulling the board directly from region 1 to region 2. Assume that the board moves at constant velocity.

Hint A.1 The net force of friction

Hint not displayed

Hint A.2 Work as integral of force

Hint not displayed

Hint A.3 Direction of force of friction

Hint not displayed

Hint A.4

Formula for

Hint not displayed

Express the net work in terms of , , , , and .

ANSWER: =

This answer makes sense because it is as if the board spent half its time in region 1, and half in region 2, which on average, it in fact did.

Part B

What is the total work done by the external force in pulling the board from region 1 to region 2? (Again, assume that the board moves at constant velocity.)

Hint B.1 No acceleration

Hint not displayed

Express your answer in terms of , , , , and .

ANSWER:

=

The Work Done in Pulling a Supertanker

Two tugboats pull a disabled supertanker. Each tug exerts a constant force of 1.90×106 , one at an angle

18.0 west of north, and the other at an angle 18.0 east of north, as they pull the tanker a distance

0.900 toward the north.

Part A

What is the total work done by the two tugboats on the supertanker?


Hint not displayed

Hint A.2 Find the work done by one tugboat

Hint not displayed

Express your answer in joules, to three significant figures.

ANSWER:

3.25×109

Work and Kinetic Energy

Two blocks of ice, one four times as heavy as the other, are at rest on a frozen lake. A person pushes each

block the same distance . Ignore friction and assume that an equal force is exerted on each block.

Part A

Which of the following statements is true about the kinetic energy of the heavier block after the push?


Hint not displayed

Hint A.2 Find the work done on each block

Hint not displayed

ANSWER:

It is smaller than the kinetic energy of the lighter block.

It is equal to the kinetic energy of the lighter block.

It is larger than the kinetic energy of the lighter block.

It cannot be determined without knowing the force and the mass of each block.

The work-energy theorem states that the change in kinetic energy of an object equals the net work done on that object. The only force doing work on the blocks is the force from the person, which is the same in both cases. Since the initial kinetic energy of each block is zero, both blocks have the same final kinetic energy.

Part B

Compared to the speed of the heavier block, how fast does the light block travel?


Hint not displayed

Hint B.2 Proportional reasoning

Hint not displayed

ANSWER:

one quarter as fast

half as fast

the same speed

twice as fast

four times as fast

Since the kinetic energy of the lighter block is equal to the kinetic energy of the heavier block, the lighter block must be moving faster than the heavier block.

Part C

Now assume that both blocks have the same speed after being pushed with the same force . What can be said about the distances the two blocks are pushed?

Hint C.1 How to approach the problem

Hint not displayed

Hint C.2 Relate the kinetic energies of the blocks

Hint not displayed

Hint C.3 Compare the amount of work done on each block

Hint not displayed

ANSWER:

The heavy block must be pushed 16 times farther than the light block.



The heavyt block must be pushed the same distance as the light block.

The heavy block must be pushed half as far as the light block.

Because the heavier block has four times the mass of the lighter block, when the two blocks travel with the same speed, the heavier block will have four times as much kinetic energy. The work-energy theorem implies that four times more work must be done on the heavier block than on the lighter block. Since the same force is applied to both blocks, the heavier block must be pushed through four times the distance as the lighter block.

Problem 6.46

A rope pulls a box a horizontal distance of 23 .

Part A

If the rope tension is 120 , and if the rope does 2500 of work on the box, what angle in figure does it make with the horizontal?

Express your answer using two significant figures.

ANSWER: =

25

Problem 6.29

A 60 skateboarder comes over the top of a hill at 4.0 and reaches 11 at the bottom of the hill.

Part A

Find the total work done on the skateboarder between the top and bottom of the hill. Express your answer using two significant figures.

ANSWER: = 3200

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