Republic of the Philippines

Mountain Province State Polytechnic College

Bontoc, Mountain Province

WORK, ENERGY, AND POWER

Module 4 of 8 Modules

General Physics

Elsa B. Daguio
CP #: 09074186867
Messenger account: Herzelle Bag-ay Daguio

Engineering Department

First Semester, School Year 2022-2023

INTRODUCTION

In the previous modules, concepts on vectors, Newton’s Laws of Motion and

Impulse and Momentum were given. These concepts are important in order for you to
relate with the given lessons in this module.

The lessons here are work, energy, and power and the law of conservation of
energy. The activities here are designed for all students, regardless of gender and
cultural background. The number of hours allotted for this module shall be 8 hours.

LEARNING OUTCOMES

At the end of the module, you should be able to:

1. define work and energy;
2. differentiate potential energy from kinetic energy;
3. define power and efficiency;
4. relate work with energy;
5. calculate the work done by a force acting on a body using work equations;
6. compute the input and output power generated by a body using power
equations;
7. solve the efficiency of power generated by a body using the given formulas;
and
8. calculate the potential energy and kinetic energy of a body applying the
law of conservation of energy.

PRETEST

Let see if you are knowledgeable with work, energy and power. Take time to
answer the following questions by encircling the letter of your answer before
proceeding to the given lessons. Submit a copy of this together with the other activities
in this module. Take note of the items that you do not know or not sure of. As you go
through the lessons, discover the correct answers and learn from them.

1. Which of the following is the equivalent unit for work?

a. Kilogram – meter
b. Newton
c. Newton – meter
d. Newton – second

2. Which of the following is the equivalent unit for energy?

a. Joules
b. Kilogram
c. Newton
d. Horsepower

3. Which of the following is not a unit for power?

a. Horsepower
b. Kilowatt
c. Newton
d. Watt

1
4. Which of the following is a form of mechanical energy?
a. Electrical energy
b. Heat energy
c. Light energy
d. Potential energy

5. Which of the following requires more work?

a. Lifting a 10 – kg load a vertical distance of 2 m
b. Lifting a 5 – kg load a vertical distance of 4 m
c. Lifting a 4 – kg load a vertical distance of 5 m
d. Lifting a 3 – kg load a vertical distance of 7 m

6. Which of the following has potential energy?

a. A boulder on top of a hill
b. A lifted heavy load
c. A stretched bow
d. All of the above

7. Which of the following has kinetic energy?

a. A book on top of a table
b. A falling rock
c. A passenger on a car
d. A rider on a horse

8. If an apple was dropped from a tree, what would be its potential energy when it
reached the ground?
a. The potential energy is zero.
b. The potential energy is half of its kinetic energy.
c. The potential energy is equal to its kinetic energy.
d. The potential energy does not change.

9. If an apple was dropped from a tree, what would be its kinetic energy when it
reached the ground?
a. The kinetic energy is zero.
b. The kinetic energy is half of its potential energy.
c. The kinetic energy is equal to its potential energy.
d. The kinetic energy does not change.

10. If an apple was dropped from a tree, what would be its kinetic energy before it
was dropped?
a. The kinetic energy is zero.
b. The kinetic energy is half of its potential energy.
c. The kinetic energy is equal to its potential energy.
d. The kinetic energy does not change.

2
LESSON 1: WORK, ENERGY AND POWER

Objectives:
At the end of the lesson, you should be able to:
1. calculate the work done by a force acting on a body using the given
equations;
2. compute the potential energy of a body using the given equations;
3. calculate the kinetic energy of a body using the given equations;
4. calculate the power generated by a body using the given equations; and
5. compute the velocity of a body in motion using the given equations.

LET’S ENGAGE

Is there a work done in lifting a barbell?

LET’S TALK ABOUT IT

Energy is the most central concept underlying all of science. Surprisingly, the
idea of energy was known to Isaac Newton and its existence was still being debated in
1850’s. Even though the concept of energy is relatively new, today we find it ingrained
not only in all branches of science, but in nearly every aspect of human society. We
are all quite familiar with energy. Energy comes to us from the sun in the form of
sunlight, it is in the food we eat, and it sustains life. Energy may be the most familiar
concept in science, yet it is one of the most difficult to define. Persons, places, and
things have energy, but we observe only the effects of energy when something is
happening – only when energy is being transferred from one place to another or
transformed from one form to another. We begin our study of energy by observing a
related concept, work.

Work is the energy transferred to or from an object by means of a force acting

on the object. Energy transferred to the object is a positive work and energy
transferred from the object is a negative work. In equation form,

3
 We do work when we lift a load against Earth’s gravity. The heavier the load or
the higher we lift it, the more work we do. If we lift two loads up one storey, we do
twice as much work as we would in lifting one load the same distance, because the
force needed to lift twice the weight is twice as great. Similarly, if we lift one load two
storeys instead of one storey, we do twice as much work because the distance is twice
as great.

Notice that the definition of work involves both a force and a distance. A weight
lifter holding a barbell weighing 1000 N over his head does no work on the barbell. He
may get really tired holding it, but if the barbell is not moved by the force he exerts, he
does no work on the barbell. Work may be done on the muscles by stretching and
squeezing them, which is force times distance on a biological scale, but this work is
not done on the barbell. Lifting the barbell, however, is a different story. When the
weight lifter raises the barbell from the floor, he is doing work on it.

Work generally falls into two categories. One of these is the work done against
another force. When an archer stretches her bowstring, she is doing work against the
elastic forces of the bow. Similarly, when you do push – ups, you do work against your
own weight. You do work on something when you force it to move against the
influence of an opposing force – often friction. The other category of work is done to
change the speed of an object. This kind of work is done in bringing an automobile up
to speed or in slowing it down.

The unit of measurement for work combines a unit of force (in Newton) with a
unit of distance (in meter). The resulting unit of work is Newton – meter (N m), also
called Joule (J) in honor of James Joule.
1 J 1 N-m
1 kJ 1000 J
1MJ 1000 kJ

Mechanical Energy

When work is done by an archer in drawing back a bowstring, the bent bow
acquires the ability to do work on the arrow. In this case, something has been
acquired that enables the object to do work. It may be in the form of a compression of
atoms in the material of an object, or a rearrangement of electric charges in the
molecules of a substance. This something that enables an object to do work is Energy.
Like work, energy is measured in Joules. It happens in many forms but we will focus
on the two most common forms of mechanical energy – the energy due to the position
of something, or the movement of something. Mechanical energy can be in the form of
either potential energy or kinetic energy, or the sum of the two.

Potential Energy

An object may store energy by virtue of its position. The energy that is stored
and held in readiness is called Potential Energy (PE) because in the stored state it
has the potential for doing work. A stretched or compressed spring for example, has a
potential for doing work. When a bow is drawn back, energy is stored in the bow. The
bow can do work on the arrow.

4
 Work is required to elevate objects against Earth’s gravity just like in the case of
a weight lifter that lifts the barbell. The potential energy due to elevated positions is
called Gravitational Potential Energy. The amount of gravitational potential energy
possessed by an elevated object is equal to the work done against gravity in lifting it.
The work done equals the force required to move it upward times the vertical distance
it is moved (remember ). The upward force required is equal to the weight,
, of the object, so the work done in lifting it through a height h is the product
mgh.

Note that the height is the distance above some chosen reference level, such as
the ground or the floor of a building. The gravitational potential energy, mgh, is
relative to that level. We can see in Figure 10.1 that the potential energy of the boulder
at the top of the ledge does not depend on the path taken to get the boulder there.

(Hewitt, 2005)
Figure 10.1: The potential energy of the 100 – N boulder with respect to the ground
below is 200 J in each case because the work done in elevating it 2m is the same
whether the boulder is (a) lifted with 100 N force, (b) pushed up the incline with 50 N of
force, or (c) lifted with 100 N of force up each 0.5 m stair. No work is done in moving it
horizontally, neglecting friction.

Kinetic Energy

Push on an object and you can set it in motion. If an object is moving, then it is
capable of doing work. It has energy of motion, or Kinetic Energy (KE). The kinetic
energy of an object depends on the mass of the object as well as its speed. It is equal
to half the mass multiplied by the square of the speed.

When you throw a ball, you do work on it to give it speed as it leaves your hand.
The moving ball can then hit something and push it, doing work on what it hits. The
kinetic energy of a moving object is equal to the work required to bring it to that speed
from rest, or the work the object can do while being brought to rest.

5
Or in equation form,

In the above equation, note the relationship between work and energy. Work
changes kinetic energy. If no change in energy occurs, then no work is done. Likewise
for potential energy ( ). Whenever work is done,
energy changes. This is the Work – Energy Theorem:

Power

The definition of work says nothing about how long it takes to do the work.
When carrying a load up some stairs, you do the same amount of work whether you
walk or run up the stairs. So why are you more tired after running upstairs in a few
seconds than after walking upstairs in a few minutes? To understand this difference,
we need to talk about how fast the work is done, or Power. Power is the rate at which
work is done. It is equal to the amount of work done divided by the time interval
during which the work is done.

A high – power engine does work rapidly. An automobile engine that delivers
twice the power of another automobile engine does not necessarily produce twice as
much work or go twice as fast as the less powerful engine. Twice the power means the
engine can do twice the work in the same amount of time or the same amount of work in
half the time. A powerful engine can get an automobile up to a given speed in less time
than a less powerful engine can.

The unit of power is the joule per second, also known as the Watt, in honor of
James Watt, the eighteenth – century developer of steam engine.
1 Watt (W) 1 J/s
1 kilowatt (kW) 1000 W
I horsepower (hp) 746 W

Examples:

1. How much work is done on a 100 – N boulder that you carry horizontally across a
10 – meter room? How much potential energy does the boulder gain?
Answer:
You do no work on the boulder moved horizontally because you apply no
force (except for the tiny bit to start and stop it) in its direction of motion. It has
also no more potential energy across the room than it has initially.

2. How much work is done on a 100 – N boulder when you lift it 1 m.? What power
is expended if you lift the boulder a distance of 1 m in a time of 1 s? What is the
gravitational potential energy of the boulder in the lifted position?

6
 Answer:
You do 100 J of work when you lift it 1 m. In order to lift the 100 N boulder, you
needed also 100 N of force. Since

( )

The gravitational potential energy of the boulder depends on its reference

level. If it is relative to the starting position, the boulder’s PE is equal to the work
done which is 100 J. If it is relative to other reference level, its PE would be some
other value.

3. What is the work done when a 20 – N force pushes a cart 3.5 m?

Solution:

( )

4. What is the work done needed to lift a 90 – N block of ice a vertical distance of 3
m? What PE does it have?
Solution:
In order to lift the 90 – N block, a force of 90 – N force is needed. From

( )

Since work changes energy,

5. Suppose the same block of ice in # 4 is raised the same vertical distance by
pushing it up a 5 – m long inclined plane using a force of 54 N, what is the work
done to push the block up the plane? What PE does it have?
Solution:

( )

7
6. What is the kinetic energy of a 3 – kg toy cart that moves at 4 m/s?
Solution:

( )( )

7. What is the kinetic energy of a 10 – kg cart when its speed increases from 4 m/s
to 10 m/s?
Solution:

( )

( )[( ) ( ) ]

8. A 400 – N force acts on a 45 - kg block that is initially at rest on a horizontal

frictionless surface. If it moves a distance of 5 meters, what will be its final
velocity?
Solution:
From work – energy equation,

( )

( ) ( )[ ( ) ]

9. Suppose that the block in # 8 moves on a horizontal surface with a roughness

coefficient of 0.20, what would be its final velocity at a distance of 5 meters?
Solution:
Remember that in Newton’s Laws of Motion, friction is an opposing force.
Thus, net force of the work done by the block will no longer be 400 N.

; The only normal force acting is the weight of the block, thus

( )( )

8
 ( )

( ) ( )[ ( ) ]

10. Suppose that the block in # 8 moves on a 30 inclined plane with a roughness
coefficient of 0.20 and the 400 – N applied force is parallel to the plane, what
would be its final velocity at a distance of 5 meters?

Solution:
Applying the concepts learned in Newton’s Laws of Motion, we should
consider all forces acting on the block.

𝑓
Net force of the work done by the block is the combination of all forces
parallel to the plane. So, .

( )

; The normal force acting on the block is the combination of all

forces perpendicular to the plane.
( )
[ ( ) ]

9
 ( )

( ) ( )[ ( ) ]

IT’S YOUR TURN

Activity 1: Copy and answer the following problems. Make sure that your handwriting
is legible. Your solutions must be organized and detailed and avoid erasures as much
as possible. Use long bond papers ( ). See Appendix A for additional content of
your first page and the rubric for scoring.
1. A 20 kg child, starting from rest, slides down a 3m high frictionless slide. How
fast is he going at the bottom? ( )
1. A 50 – kg barbell is lifted at a height of 1.4 m from the floor in 1.2 seconds. What
is the work done? How much power is expended? ( )
2. A 60 kg block at rest was pushed by a 100 N force on a frictionless horizontal
surface.
a. What is the kinetic energy of the block at a distance of 8 meters? ( )
b. What is the velocity of the block at a distance of 8 meters? ( )

Rubric:
Insufficient Fair Good Very Good Excellent
( ) ( ) ( ) ( ) ( )
All parts of Few parts of Some parts of Most parts All parts of
the written the written the written of the the written
Accuracy solution are solution are solution are written solution are
incorrect. correct. correct. solution are correct.
correct.
No work is Few parts of Some parts of Most parts All parts of
completed. the written the written of the the written
Completion solution are solution are written solution are
completed. completed. solution are completed.
completed.
None of the Few Some of the Most of the All writings
writings are writings are writings are writings are are legible
Neatness
legible with legible with legible and is legible and and is
and
many many neat with is neat with incredibly
Legibility
smudges. smudges. several a few neat with no
smudges. smudges. smudges.
All parts of Few parts of Some parts of Most parts All parts of
the written the written the written of the the written
solution are solution are solution are written solution are
Organization
confusing. organized. organized. solution are well-
well- organized.
organized.

10
LESSON 2: CONSERVATION OF ENERGY

Objectives:
At the end of the lesson, you should be able to:
1. calculate the efficiency of the work done by an object;
2. compute the force acting on an object applying the law of conservation of
energy; and
3. determine the velocity of a moving body applying the law of conservation of
energy.

LET’S ENGAGE

What is the Law of Conservation of Energy?

LET’S TALK ABOUT IT

The Law of Conservation of Energy states that “Energy cannot be created nor
destroyed; it can be trasformed from one form to another, but the total amount of energy
never changes”. More important than knowing what energy is, is the understanding
how it behaves – how it transforms. We can better understand nearly every process or
change that occurs in nature if we analyze it in terms of a transformation of energy
from one form to another.

As you draw back the stone in a slingshot, you do work when you stretch the
rubber band. The rubber band then has potential energy. When released, the stone
has kinetic energy equal to this potential energy. It delivers this energy to its target,
perhaps a wooden fence post. The slight distance the post is moved multiplied by the
average force of impact doesn’t quite match the kinetic energy of the stone. The energy
score doesn’t balance. But if you investigate further, you’ll find that both the stone
and the fence post are a bit warmer. By how much? By the energy difference. Energy
changes from one form to another, it transforms without net loss or net gain.

When you consider any system in its entirety, whether it is as simple as a

swinging pendulum, as shown in Figure 11.1, or as complex as an exploding galaxy,
there is one quantity that does not change: energy.

(Sawant, 2018)
Figure 11.1: The PE of the pendulum bob at its highest point is equal to the KE of the
bob at its lowest point. Everywhere along its path, the sum of PE and KE is the same.

11
 Another example of energy transformation can be seen in Figure 11.2. The PE of
the ball before falling is equal to the KE of the ball before hitting the ground. As the
ball falls, the sum of PE and KE is the same. Or, in equation form

J
J

J
J

J
J

Figure 11.2: Conservation of energy on Free – falling bodies

Note: The total mechanical energy before motion is equal to the total mechanical
energy after motion.

Machines

A machine is a device used to multiply forces or simply to change the direction

of forces. The concept that underlies every machine is the conservation of energy.
Consider one of the simplest machines, the lever, shown in Figure 11.3. At the same
time we do work on one end of the lever, the other end does work on the load. We see
that the direction of force is changed. If we push down, the load is lifted up. If the heat
from friction is small enough to neglect, the work input will be equal to the work
output.

Since work equal force times distance, we can say

( ) ( )

A little thought will show that the pivot point, or fulcrum, of the lever can be
relatively close to the load. Then a small input force exerted through a large distance
will produce a large output force over a correspondingly short distance. In this way, a
lever can multiply forces. However, no machine can multiply work or energy.

12
 Consider the ideal weightless lever in Figure 11.3. The child pushes down 10 N
and lifts an 80 – N load. The ratio of output force to input force for a machine is called
the mechanical advantage. Here the mechanical advantage is ( )⁄( ), or 8.
Notice that the load moves only one – eighth of the distance the input force moves.
Neglecting friction, the mechanical advantage can also be determined by the ratio of
input distance to output distance.

(Hewitt, 2005)
Figure 11.3: The output force (80 N) is eight times the input force (10 N), while the output
distance is one – eighth ( ⁄ ) of the input distance (1 m).

Three common ways to set up a lever are shown in Figure 11.4. A type 1 lever
has the fulcrum between the force and the load, or between input and output. This
kind of lever is commonly seen in a playground seesaw with children sitting on each
end of it. Push down on one end and you lift a load at the other. You can increase
force at the expense of distance. Note that the directions of input and output are
opposite.

(Hewitt, 2005)
Figure 11.4: The three basic type of levers.

For a type 2 lever, the load is between the fulcrum and the input force. To lift a
load, you lift the end of the lever. One example is placing one end of a long steel bar
under an automobile frame and lifting on the free end to raise the automobile. Again,
force on the load is increased at the expense of distance. Since the input and output
forces are on the same side of the fulcrum, the forces have the same direction.

13
 In the type 3 lever, the fulcrum is at one end and the load is at the other. The
input force is applied between them. Your biceps muscles are connected to the bones
in your forearm in this way. The fulcrum is your elbow and the load is in your hand.
The type 3 lever increases distance at the expense of force. When you move your
biceps a short distance, your hand moves a much greater distance. Notice that the
input and output forces are on the same side of the fulcrum and therefore they have
the same direction.

A pulley is basically a kind of lever that can be used to change the direction of
a force. Properly used, a pulley or system of pulleys can multiply forces.

The single pulley in Figure 11.5a behaves like a type 1 lever. The axis of the
pulley acts as the fulcrum, and both lever distances (the radius of the pulley) are equal
so the pulley does not multiply force. It simply changes the direction of the applied
force. In this case, the mechanical advantage equals 1. Notice that the input distance
equals the output distance the load moves.

In Figure 11.5b, the single pulley acts as a type 2 lever. Careful thought will
show that the fulcrum is at the left end of the “lever” where the supporting rope makes
contact with the pulley. The load is suspended halfway between the fulcrum and the
input end of the lever, which is on the right end of the “lever”. Each newton of input
will support two newtons of load, so the mechanical advantage is 2. This number
checks with the distances moved. To raise the load 1 m, the woman will have to pull
the rope up 2 m. We can say the mechanical advantage is 2 for another reason: the
load is now supported by two strands of rope. This means each strand supports half
the load. The force the woman applies to support the load is therefore only half of the
weight of the load.

(Hewitt, 2005)
Figure 11.5: A pulley can (a) change the direction of a force as input is exerted
downward and load moves upward, (b) multiply force as input is now half the load, and
(c) when combined with another pulley, both change the direction and multiply force.

The mechanical advantage for simple pulley systems is the same as the number
of strands of rope that actually support the load. In Figure 11.5a the load is supported
by one strand and the mechanical advantage is 1. In Figure 11.5b the load is
supported by two strands and the mechanical advantage is 2. Can you use this rule to
state the mechanical advantage of the pulley system in Figure 11.6c?

The mechanical advantage of the simple system in Figure 11.5c is 2. Notice that
although three strands of rope are shown, only two strands actually support the load.
The upper pulley serves only to change the direction of the force.

14
 No machine can put out more energy than is put into it. No machine can create
energy. A machine can only transfer energy from one place to another or transform it
from none form to another.

Efficiency

The previous examples of machines were considered to be ideal. All the work
input was transferred to work output. An ideal machine would have 100% efficiency.
In practice, 100% efficiency never happens, and we can never expect it to happen. In
any machine, some energy is transformed into atomic or molecular kinetic energy –
making the machine warmer. We say this wasted energy is dissipated as heat.

When a simple lever rocks about its fulcrum, or a pulley turns about its axis, a
small fraction of input energy is converted to thermal energy. We may put in 100 J of
work on a lever and get out 98 J of work. The lever is then 98% efficient and we lose
only 2 J of work input as heat. In a pulley system, a larger fraction of input energy is
lost as heat. For example, if we do 100 J of work, the friction on the pulley as they
turn and rub on their axle can dissipate 40 J of heat energy. So the work output is
only 60 J and the pulley system has an efficiency of 60%. The lower the efficiency of
the machine, the greater the amount of energy wasted as heat.

Efficiency can be expressed as the ratio of useful work output to total work
input.

An inclined plane is a machine. Sliding a load up an incline requires less force

than lifting it vertically. Figure 11.6 shows a 5 – m inclined plane with its high end
elevated by 1 m. Using the plane to elevate a heavy load, we push the load five times
farther than we lift it vertically. If friction is negligible, we need to apply only one – fifth
of the force required to lift the load vertically. The inclined plane shown has a
theoretical mechanical advantage of 5.

(Hewitt, 2005)
Figure 11.6: Pushing the block of ice 5 times farther up the incline than the vertical
distance it’s lifted requires a force of only one – fifth its weight. Whether pushed up the
plane or simply lifted, the ice gains the same amount of PE.

15
 A block of ice sliding along an icy plank, or a horse – pulled cart with well –
lubricated wheels, might have an efficiency of almost 100%. However, when the load is
a wooden crate sliding on a wooden plank, both the actual mechanical advantage and
the efficiency will be considerably less. Efficiency can also be expressed as the ratio of
actual mechanical advantage to theoretical mechanical advantage. Efficiency will
always be a fraction less than 1.

Examples:

1. At one point in its fall, a falling object has a kinetic energy of 5 J and a potential
energy of 10 J (relative to the floor). It continues to another point where its
potential energy is 3 J. What is its kinetic energy at this point?
Solution:
Since the sum of the kinetic energy and potential energy of an object is the
same along its path, then

2. A 14300 kg airplane is flying at an altitude of 497 m at a speed of 216 km/h.

What is the airplane’s total mechanical energy? What would be the velocity in
km/h of the airplane at an altitude of 450 m?
Solution:

( )( )
⁄

( )( ) ( )( )

At an altitude of 497 m, the total mechanical energy is J. For an

altitude of 450 m, the total mechanical energy will still be J. Thus,

( ) ( )( )

⁄ ( )( )

16
3. A lever is used to lift a heavy load. When a 50 – N force pushes one end of the
lever down 1.2 m, the load rises 0.2 m. What is the weight of the load?
Solution:
( ) ( )
( ) ( )

4. What is the efficiency of a machine that has a useful energy output of 220 J when
the work input is 300 J?
Solution:

( )

5. What is the theoretical mechanical advantage of a 5 – m long inclines plane that

has a high end 1 m above the ground? What is the actual mechanical advantage
if 100 N of effort is needed to push a block of ice that weighs 400 N up the plane?
What is the efficiency of the inclined plane?
Solution:

( )

6. A 700 – kg roller coaster car is at the top of a hill 60 m high. A rider on the car
wants to know the velocities of the car at various points along the car’s path.
a. What is the velocity of the car when it reached the point where the height is
40 meters?
b. What is the velocity of the car when it reached the point where the height is
35 meters?
c. What is the velocity of the car when it reached the point where the height is
10 meters?

17
Solution:
a. Given: ,
Req’d: at 40 m
Applying the concept on Figure 11.2:

( ) ( )

( ) ( ) ( )

( )( ) ( )( ) ( )( )

b. Given: ,
Req’d: at 35 m

( ) ( )

( ) ( ) ( )

( )( ) ( )( ) ( )( )

c. Given: ,
Req’d: at 10 m

( ) ( )

( ) ( ) ( )

( )( ) ( )( ) ( )( )

18
IT’S YOUR TURN

Activity 2: Copy and answer the following problems. Make sure that your handwriting
is legible. Your solutions must be organized and detailed and avoid erasures as much
as possible. Use long bond papers ( ). See Appendix A for additional content of
your first page and the rubric for scoring.
1. Willie E. Coyote is trying to drop a 10 kg boulder off a 10 m high cliff to hit the
Roadrunner eating a bowl of birdseed on the road below. He wants to know the
speed of the boulder at various points above the road.
a. What would be the velocity of the boulder at 8.0 m above the road? ( )
b. What would be the velocity of the boulder at 6.0 m above the road? ( )

2. In raising a 5000 – N piano with a pulley system, the workers note that for every
2 m or rope pulled down, the piano rises 0.4 m.
a. Ideally, how much force is required to lift the piano? ( )
b. If the workers actually pull with 2500 N of force to lift the piano, what is the
efficiency of the pulley system? ( )

Rubric:
Insufficient Fair Good Very Good Excellent
( ) ( ) ( ) ( ) ( )
All parts of Few parts of Some parts of Most parts All parts of
the written the written the written of the the written
Accuracy solution are solution are solution are written solution are
incorrect. correct. correct. solution are correct.
correct.
No work is Few parts of Some parts of Most parts All parts of
completed. the written the written of the the written
Completion solution are solution are written solution are
completed. completed. solution are completed.
completed.
None of the Few Some of the Most of the All writings
writings are writings are writings are writings are are legible
Neatness
legible with legible with legible and is legible and and is
and
many many neat with is neat with incredibly
Legibility
smudges. smudges. several a few neat with no
smudges. smudges. smudges.
All parts of Few parts of Some parts of Most parts All parts of
the written the written the written of the the written
solution are solution are solution are written solution are
Organization
confusing. organized. organized. solution are well-
well- organized.
organized.

19
POST ASSESSMENT
Now let’s test if you have learned something from this module. Copy and answer
the following problems. Make sure that your handwriting is legible. Your solutions
must be organized and detailed and avoid erasures as much as possible. Use long
bond papers ( ). See Appendix A for additional content of your first page and
the rubric for scoring.
1. What power is required to lift a elevator at a constant speed of ⁄ ?
( )
1. A 100 N box was pulled by a 200 N horizontal force on a horizontal table
with a roughness coefficient of 0.20. ( )
a. What is the work done by the box at a distance of 6 meters?
b. What is the velocity of the block at a distance of 6 meters?
2. A 60 kg block at rest was pushed by a 400 N force on a inclined plane with a
roughness coefficient of 0.15. The force is applied parallel to the plane.
a. What is the work done by the block at a distance of 10 meters? ( )
b. What is the velocity of the block at a distance of 10 meters? ( )

3. A 500 – kg roller coaster car is pulled to the top of a hill 45 m high and arrives at
the top with zero speed. ( )
a. How much work is done by the chain that pulls the car to the top?
b. How fast will the car be going when it gets back to ground level, 45 m below?
c. How fast will the car go at a point 29 m above ground?

Rubric:
Insufficient Fair Good Very Good Excellent
( ) ( ) ( ) ( ) ( )
All parts of Few parts of Some parts of Most parts All parts of
the written the written the written of the the written
Accuracy solution are solution are solution are written solution are
incorrect. correct. correct. solution are correct.
correct.
No work is Few parts of Some parts of Most parts All parts of
completed. the written the written of the the written
Completion solution are solution are written solution are
completed. completed. solution are completed.
completed.
None of the Few Some of the Most of the All writings
writings are writings are writings are writings are are legible
Neatness
legible with legible with legible and is legible and and is
and
many many neat with is neat with incredibly
Legibility
smudges. smudges. several a few neat with no
smudges. smudges. smudges.
All parts of Few parts of Some parts of Most parts All parts of
the written the written the written of the the written
solution are solution are solution are written solution are
Organization
confusing. organized. organized. solution are well-
well- organized.
organized.

20
APPENDIX A

21
REFERENCES

Hewitt, P. G. (2007). Conceptual physics (10th ed.) Jurong, Singapore: Pearson

Education South Asia Pte Ltd.

Serway, R. A., & Faughn, J. S. (1989). College physics (2nd ed.). New York, New York:
Sauders College Publishing.

Baron, L. (n. d.) Body building, powerlifting, and weightlifting sports. Retrieved from
https://www.verywellfit.com/bodybuilding-powerlifting-and-weightlifting-
3498670

Sawant, S. (2018). Conservation of energy. Retrieved from

https://www.topperlearning.com/answer/explain-how-the-law-of-conservation
-of-energy-holds-true-for-three-different-position-of-the-bo/7r3i6w22

22