MECHANICAL ENERGY

CONSERVATION OF
MECHANICAL ENERGY

for SCIENCE Grade 9
Quarter 4 / Week 4

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FOREWORD

This Self Learning Kit is prepared for learners to develop their ability in
describing energy that plays an important role in our daily life.

In this learning kit, the transformations of mechanical energy and its
conservation will be studied conceptually and mathematically as applied in
many natural events as well as in the working principles of man-made
structures such as rides and electric power plants.

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OBJECTIVES

K: Explain energy transformation in the Law of Conversation of Mechanical
Energy

S: Create a device that show conservation of mechanical energy
A: Ascertain that the total mechanical energy remains the same during any

process.

LEARNING COMPETENCY conservation of

Perform activities that demonstrate
mechanical energy. S9FE-IVd-40

I. WHAT HAPPENED

PRE-TEST

True or False

Directions: Write TRUE if the statement is correct or FALSE if it is incorrect.

1. The energy stored in a stretched spring is called kinetic energy.
2. The total mechanical energy of a body is the sum of its potential energy

and kinetic energy.
3. When a basketball and a pingpong ball are thrown with the same

velocity, the kinetic energy of the basketball is equal to the kinetic
energy of the pingpong ball.
4. The mechanical energy of a free-falling body is conserved.
5. When the object falls the kinetic and potential energy is the same.
6. The potential energy of the object at the top is the lowest.
7. In conservation of mechanical energy, ME = PE – KE.
8. Kinetic energy is stored energy.
9. Electrical energy – sound energy is the energytransformation in a light
bulb.
10. PE = ME – KE, takes place in conservation of mechanical energy.

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II. WHAT I NEED TO LEARN

DISCUSSION
Forms of Energy

Energy is the name of the game. Everything exists or cease to exist because of
its presence or absence. It is stored in different forms and can transfer and/or
transform. It can be transferred without being transformed. It can also be
transformed without being transferred. It can also be transformed during transfers.

In general, the energy acquired by objects upon which work is done is known
as mechanical energy. You have learned in Grade 8 Science that mechanical energy
fall under two categories:

Table 1. Different forms of Mechanical Energy

Table 2. Mechanical Potential and Kinetic Energy Equation

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The evidence and varied uses of the different energy forms are everywhere. Its
flow causes change through heat and work.

Be it energy moving through the food chain or an electric power plant, energy
can never be created from nothing nor can it be destroyed into nothing. Energy is simply
transformed from one form to another or transferred from one system to another. It
flows from a source (serving as input system) into an output system during transfers
and/or transformations.

Figure 1. Energy transformation in a lit electric lamp.

Figure 2. In a plugged television, electrical energy is converted into radiant, heat and sound energies.

Figure 3. During photosynthesis, the sun’s radiant energy is converted into chemical energy

You just identified the different energy forms and the transformation it undergo.
Indeed, when these energy got transferred or transformed, work and heat plus other energy
forms like sound and light were produced. Some of these energy can also be stored in other
forms. In general, when you made each toy or object to operate in the activity and set it
to move then

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the physics behind the toys caused transformations of mechanical energies from potential
to kinetic or from kinetic to potential.

Now ponder these questions. What are the similarities in the mechanical energy
forms present in a stretched bowstring and in an elevated volume of water? What
mechanical work can possibly be done by the transformations of these mechanical
energies?

Figure 4. Comparison of mechanical energy in a stretched bow and a waterfalls

Activity 1
Construction of simple turbine unit

(Adapted from the Energy of Moving Water Student Guide from www.NEED.org)

Materials Needed:
plastic folder or acetate
permanent marker pen ruler
or tape measure pair of
scissors
cutter
juice drink straw
hot melt glue or super glue (cyanoacrylate adhesive) masking tape
thread
5-10 pcs paper clips
2 1.5-Liter plastic bottle 1
push pin
3-inch nail
2 3-Liter ice cream container
2-Liter bottled tap water supply hand towel or rag funnel activity
sheet / science notebook

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Safety Precautions:
• Danger of injury from the pair of scissors and cutter.
• Danger of eye or skin injury from glue
• Use of water container for collecting water.
• Use of towel or rag to dry off wet surfaces.
• Follow all safety lab rules

Procedure:
A. Construction of the Turbine Model
1. Prepare 8 blades for the turbine.
2. Cut 2 inch by 1 inch strips of plastic folder or acetate. Shape it any way you want.

Figure 5. a) shaped strips for turbine blades

3. Glue the blades to the middle of the straw similar to the sample in Fig. 5b). The straw will
serve as the shaft of the turbine.

Figure 5. b) the turbine model blade assembly

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4. Make a turbine holder using one of the plastic bottles. Use a push pin then a 3-in nail
to make holes at a 10-cm height to hold the straw. Ensure that the turbine can rotate
freely. If needed, make some plastic stopper to hold the turbine in place.

Figure 5. c) the turbine model on its mount

Figure 5.c) the turbine model on its mount4. Tie a meter-long thread around the
turbine shaft (straw). Secure the knot to the shaft with a tape. Loop the hanging
end of the string and hook the paper clips on it.

5. Position the turbine model on a table with the hanging paper clips free to
move.

6. Without needing other additional materials, try the methods you can right
away do. This will also help you test the functionality and durability of your
turbine model.

7. Reinforce the turbine holder or strengthen the blades
with melted hot glue if needed. Adding the watery super
glue may just loosen the already set bond between the
blades and the straw.

8. Remove the string and the paper clips from the straw to
have the turbine model ready for the Hydropower activity.

Figure 6

B. Water Reservoir Model Construction

1. From the bottom of the bottle, measure and mark with dots the 5-
cm, 10-cm, 15-cm, and 20-cm spots. These dots should lie along the
same vertical line and would be the exit points. Across these, make
horizontal lines as tail water levels, ht.

Figure 7.a

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2. Use the push pin to make a hole on each dot. Then put masking tape over each hole.
Fold the top as flap for pulling.
3. Make another horizontal line 5 centimeters above the 20-cm hole and mark as the
head water level, hw of the stored water.
4. Determine the stored water’s Head of Flow, H by taking the difference
between the head water level and the tail water level as indicated in the equation = ℎw −
ℎt
5. Fill the bottle with water up to the 25-cm mark. Elevate this bottle on an inverted ice-
cream container with its holed-side facing the other water container where the turbine model
is.

Figure 7 b) water reservoir and turbine assembly, and Figure 7 c) range measurement

6. Line with masking tape the back of a ruler for easier readings. Use the ruler to
measure the falling water’s maximum range (horizontal distance
between the bases of the hole and the point the projected water hits the blade).

7. Examine the water reservoir with the turbine model assembly and be familiar with its
operation. Reposition the turbine when needed.

C. Mechanical Energy in Hydropower
1. Remove the masking tape from the 5-cm hole to release the water. Be ready to

reposition the water turbine model such that the nearest blade hit by the projecting
water is in the horizontal position. Cover the hole with your finger or with a tape
when needed.
2. Measure the maximum range of the water and record this result in Table 3.
3. Uncover again the 5-cm hole and observe the projecting water as well as the
movement of the turbine blades.

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4. Cover again the 5-cm hole. Use the funnel and the bottled water supply to refill the
water reservoir up to the 25-cm mark.

5. Repeat steps 1 to 4 for a total of three trials. Compute and record the average range.

6. Dry the wet surfaces and check the tape hole covers.

7. Follow steps 1 to 6 for the 10-cm, 15-cm, and 20-cm holes.

8. Water conservation tip. Reuse the water collected on the pan. Use the funnel to
transfer water from the collecting container back into the water reservoir model or
the water supply bottle.

Table 3. Effect of the Water’s Head of Flow on the Water Range

Head Tail Stored Range Trial (cm) Average
Water Water Waters 123 Range
level, hw level, ht Height or (cm)
(cm) (cm) Head of
Flow (cm)
Equation: H

= hw – ht

25 5 20
25 10
25 15
25 20

Question:

1. What mechanical energy transformations took place when water got projected out of
the holes?

2. What was the effect of the stored water’s head of flow to its range?
3. How would you explain this effect in terms of energy transformation?

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Figure 8. Illustration on the main parts of a HEP Plant courtesy of www.NEED.org

The activity model represents Hydroelectric Power (HEP) Plant.
A typical Hydroelectric Power Plant has three main parts as shown below:

1) the water reservoir
2) the dam
3) the power plant (turbines and generators)

Just like the stretched bowstring and the elevated waterfalls, the stored water in the reservoir
has potential energy. When water is made to flow down the penstock, the potential energy
changes into kinetic energy. The faster the flow carries greater power, exerting a greater force in
rotating the turbine.

Conservation of Mechanical Energy in Free Falling Object

The sum of the kinetic and potential energies of a system constitutes mechanical energy. In
a conservative system, the total mechanical energy is constant. In this system, only conservative
forces are present and, therefore, a decrease in potential energy is equal to an increase in kinetic
energy, and vice versa. This is now expressed in a law called the law of conservation of mechanical
energy which states that:

The sum of the kinetic energy and potential energy in a conservative system is constant and
equal to the total mechanical energy of the system.

In symbols we MET = PE + KE

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Activity 2
Look at Fig. 9 below showing the position of a free falling body. Using the data in
the figure, answer the following questions:
1. What is the speed of the object when it is still held at the starting point?
2. What happens to the speed of the object as it falls?
3. What is the change in velocity per unit time or the acceleration of the object?

Fig. 2.2 An object held a certain height is released
4. What is the total distance of the object from the ground when it is at the starting

point (t = 0 s)?
5. What happens to the object’s distance from the ground as it falls?

Did you observe that the speed of the object increased as it falls? The speed
increased at the rate of 9.8 m/s every second or its acceleration was
9.8 m/s2. Do you remember that this is the acceleration due to gravity?

Did you also observe that the total distance of the object from the ground at the
initial position was 78.4 m, and as the object fell, its distance from the ground decreased?

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Activity 3

Now let us determine what happens to the free falling object’s kinetic energy and
potential energy.

1. Study the solution in determining the kinetic energy and the potential energy at t = 0
s and t = 1 s. Then, compute the KE and PE at the other remaining positions. Enter
your results in the summary in Table 2.1 (Assume mass of the object is 1.0 kg).

2. Compute also the change in PE and the change in KE at every position and enter
results in Table 4.

Example 1

At t = 0 s, the object is 78.4 m from the ground. Assuming that the mass of the object is 1
kg, and using the equations for PE, we have

PE = mgh
= (1 kg)(9.8 m/s2 )(78.4 m)
= 768.32 J

The KE at t = 0 s is,

KE = ½ mv2
= ½ (1kg)(0)2
=0

The total mechanical energy of the free falling object at t = 0s is

TME = PE + KE
= 768.32 + 0
= 768.32 J

At t = 1 s, the potential energy is,

PE = mgh
PE = (1 kg)(9.8 m/s2)(78.4 m –4.9 m) PE =
(9.8kg m/s2)(73.5 m)
PE = 720.30 J

The kinetic energy at t = 1 s is,

KE = ½ mv2
KE = ½(1 kg)(9.8 m/s)2 KE
= 48.02 J

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The total mechanical energy is,

TME = PE + KE

TME = 720.30 J + 48.02 J
TME = 768.32 J

Table 4. Summary of the Mechanical Energy of a Free Falling Body

Time (s) PE (J) KE (J) TME (PE + KE) J Change in Change in
KE (J)
PE (J) 0
48.02
0 768.32 0 768.32 0

1 720.30 48.02 768.32 48.02

2

3

4

Using the data on Table 4 of a free falling object, answer the following questions:

1. What happens to the potential energy as the object freely falls?
2. What happens to the kinetic energy as the object freely falls?
3. Compare the change in potential energy with the change in kinetic energy as the

object freely falls.
4. Describe the total mechanical energy as the object freely falls.
5. Is mechanical energy conserved? Explain your answer.

III. WHAT I HAVE LEARNED

POST TEST

MULTIPLE CHOICE

Directions: Read each question. Choose the letter of the correct answer and write it in your
notebook.

Refer to this situation in answering questions 1-3.
An object falls freely from a certain height.

1. Which of the following happens to the object? It

a. loses PE and gains KE. c. loses both PE and KE.

b. gain PE and loses KE. d. gains both PE and KE.

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2. The PE of the object at the highest point compared to its KE at the lowest pointis

a. lesser. c. equal.

b. greater. d. not related.

3. The total mechanical energy of the object at the highest point compared to its total mechanical
energy at the lowest point is

a. lesser. c. equal.

b. greater. d. not related.

4. An object lifted to a height of 5 meters gained 1000 J of potential energy. Then, it is allowed
to freely fall. What is its kinetic energy when it hits the ground?

a. zero J c. 5000 J

b. 1000 J d. 50000 J

5. What is the energy of a motorcycle moving slowly at the top of a hill?

a. entirely kinetic c. entirely gravitational

b. entirely potential d. both kinetic and potential

6. Which event is explained in the sequence of energy changes shown in the diagram
below?

a. a headlight is on c. a turbine spins

b. electric current powers a flat iron d. gasoline burns to run a jeepney

7. Which event illustrates the direct transformation of potential to kinetic energy?
a. A basketball player catches a flying ball.
b. A Kalesa moves from rest.
c. Kathy’s arrow isreleased from its bow.

d. The spring mechanism of a toy is rotated until it locked.

8. Which sequence of energy transformation best describes what happens when you switch on
your battery-run radio?
a. Mechanical Energy  Electrical Energy  Sound Energy
b. Mechanical Energy  Chemical Energy  Sound Energy
c. Chemical Energy  Electrical Energy  Sound Energy
d. Chemical Energy  Mechanical Energy  Sound Energy

9. Which event illustrates the direct transformation of potential to kinetic energy?
a. A volleyball player blocks an incoming ball.
b. A sleeping cow stirs awake.
c. The wide-open spring door closes slowly.

d. The spring of a broken toy shoots up.

10. If air resistance is zero, the kinetic energy of a falling object at the lowest position is its
potential energy at the highest position.

a. less than c. greater than

b. equal to d. not related to

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REFERENCES

Alvarez, Liza A., et.al. (2014). Science 9 Learner’s Module. DepEd. Rabago, Lilia M,
Ph.D.,et.al, Science and Technology 9, Vibal Group Inc. Project Ease, Physics module
11, Work, Enegry, Power and Machines

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DEPARTMENT OF EDUCATION SCHOOLS
DIVISION OF NEGROS ORIENTAL

SENEN PRISCILLO P. PAULIN, CESO V
Schools Division Superintendent

FAY C. LUAREZ, TM, Ed.D, Ph.D
OIC - Assistant Schools Division Superintendent Acting CID

Chief

NILITA L. RAGAY, Ed.D.
OIC - Assistant Schools Division Superintendent

ROSELA R. ABIERA
Education Program Supervisor – (LRMDS)

ARNOLD R. JUNGCO
PSDS– Division Science Coordinator

MARICEL S. RASID
Librarian II (LRMDS)

ELMAR L. CABRERA
PDO II (LRMDS)

JEOFEL R. PIALAGO
Writer/Illustrator

STEPHEN C. BALDADO
HELBERT P. OJARIO
Lay-out Artists

ALPHA QA TEAM

ZENAIDA A. ACADEMIA ADELINE
FE D. DIMAANO VICENTE B.
MONGCOPA FLORENTINA P.
PASAJINGUE

BETA QA TEAM

ARNOLD D. ACADEMIA
ZENAIDA A. ACADEMIA
ADELINE FE D. DIMAANO
ROWENA R. DINOKOT GENEVA
FAYE L. MENDOZA VICENTE B.

MONGCOPA
FLORENTINA P. PASAJINGUE

DISCLAIMER

The information, activities and assessments used in this material are designed to provide
accessible learning modality to the teachers and learners of the Division of Negros Oriental. The
contents of this module are carefully researched, chosen, and evaluated to comply with the set
learning competencies. The writers and evaluator were clearly instructed to give credits to
information and illustrations used to substantiate this material. All content is subject to copyright
and may not be reproduced in any form without expressed written consent from the division.

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SYNOPSIS
Have you ever thought how the concepts of mechanical energy and its conservation is

applied to many natural events on real life situations? The conservation of mechanical energy
provides the principles on natural and man
– made structures that are being utilized by human being.

This SLK is designed to understand this concept.

ABOUT THE AUTHOR
Jeofel R. Pialago holds Bachelor’s Degree in Secondary Education
major in Mathematics at Foundation University, Dumaguete City. He also
have units in Physics at University of San Carlos, Talamban Campus.
Currently, he is teaching at Siaton Science High School, Mantuyop,
Siaton, Negros Oriental.

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