Unit 1 MODULE 2WORK and ENERGY

What is WORK?In physics, work is an abstract

related to energy. When work is done it is accompanied by a change in energy. When work is done by an object it loses energy and when work is done on an object it gains energy.

WORK IS DONE if the object you push moves a distance in the direction towards which you are pushing.

NO WORK IS DONE if the force you exert does not make the object move.

NO WORK IS DONE if the force you exert does not make the object move in the same direction as the force you exerted.

Work is done when the force (F) applied to the object causes the object to have a displacement (d) in the same direction as the force applied.

A GIRL IS PULLING HER TOY CAR

• Yes, the situation is an example of work. The work is done by the girl on the cart. The force exerted by the girl in pulling the toy car is in the same direction as the distance covered when the force is applied.

A MAN IS LIFTING A BOX TO BE PLACED ON A TABLE

• Yes, the situation is an example of work. The work is done by the man on the box. The force exerted by the man is upward and the box is displaced upward.

A GIRL CARRYING A BAG WALKS DOWN THE STREET

•No, the situation is not an example of work. There is force (the shoulder pushes up the bag) and there is displacement (the bag is moved horizontally).

•However, the line of action of the force and the displacement are not parallel but perpendicular. The distance covered is not along the direction of the applied force.

A MANGO FRUIT FALLING FROM THE BRANCH

• Yes, the situation is an example of work. The work is done by the force of gravity on the mango. In this case, the mango loses energy.

REVIEWWORK IS DONE OR NO WORK IS

DONE1. A teacher applies a push on the

wall and become exhausted.2. A book falls off a table and free

falls to the ground.• A rocket accelerates through

space.

CALCULATING WORKWork is done when the force(F) applied to the object causes the object to have a displacement (d) in the same direction as the force applied.

CALCULATING WORKThe symbol for work is a capital W. The work done by a force can be calculated as

W= Fd

UNIT FOR WORK

W= FdUnit of work = unit of force x unit of displacementUnit of work = N m

Unit of work = Nm or joules, J

The unit, joule (J) is named after the English physicist James Prescott Joule. This is also a unit of energy. One (1) Joule is equal to the work done or energy expended in applying a force of one Newton through a distance of one meter.

Example 1:Suppose a woman is pushing a grocery cart with a 500 Newton force along the 7 meters aisle, how much work is done in pushing the cart from end to end of the aisle to the other.

W = FdW = 500 N (7m)W = 3500 NmW = 3500 J

Example 2:In a baseball game, Lyren hit the ball with a force of 25 newtons. This sent the ball flying through 400 meters in the midfield. How much work did Lyren do on the ball?

W = FdW = 25 N (400 m)W = 10 000 NmW = 10 000 J

Example 3:A book of mass 1 kg is on the floor. If the book is lifted from the floor to the top shelf which is 2 meters from the floor, how much work is done?

W = FdW = mghW = 1 kg (9.8 m/s2)(2 m)

W = 19.6 Nm or J

Example 4:A force of 500 N is needed to push a cabinet across the lot. Two students push the cabinet 5 m. How much work is done?

W = FdW = 500 N (5 m)W = 2500 NmW = 2500 J

Example 5:Leo uses an force of 15 N to push a grocery cart a distance of 4 meters. How much work does he do?

W = FdW = 15 N (4 m)W = 60 NmW = 60 J

Example 6:A force of 50 N is used to lift a box to a height of 3 m?

W = FdW = 50 N (3 m)W = 150 NmW = 150 J

Example 7:Joanne picks up and balances a one-peso coin on the tip of her fingers 20 cm from the top of a table? What is the work done?

Kinetic Energy • The energy of a moving object is

called energy of motion or kinetic energy (KE). The word kinetic comes from the Greek word kinetikos which means moving. Kinetic energy quantifies the amount of work the object can do because of its motion.

• The plastic or rubber ball you

pushed to hit an empty plastic bottle earlier has kinetic energy. The force applied caused the ball to accelerate from rest to a certain velocity, v. In Module 1, you learn that acceleration is the rate of change in velocity.

• This shows that the work done in accelerating an object is equal to the kinetic energy gained by the object. 𝐾𝐸= ½ 𝑚𝑣2

• From the equation, you can see that the kinetic energy of an object depends on its mass and velocity.

•What will happen to the KE of an object if its mass is doubled but the velocity remains the same? How about if the velocity is doubled but the mass remains the same?

As you have learned in Module 1, the unit for mass is kg while for velocity it is meter per second. unit of KE = unit of mass x unit of velocityunit of KE = kg (m/s)2

unit of KE = kg m2/s2

But, kg m/s2 = 1 Newton, N

unit of KE = Nm or Joules, J

Example 1A 1000 kg car has a velocity of 17 m/s. What is the car’s kinetic energy?KE = ½ mv2

KE = ½ (1000 kg)(17 m/s)2

KE = ½ (1000 kg)(17 m/s)2

KE = ½ (1000 kg)(289 m2/s2) KE = ½ (289 000 kg m2/s2 ) KE = 144 500 Nm or Joules, J

Example 1A 2000 kg car has a velocity of 17 m/s. What is the car’s kinetic energy?KE = ½ mv2

KE = ½ (2000 kg)(17 m/s)2

KE = ½ (2000 kg)(17 m/s)2

KE = ½ (2000 kg)(289 m2/s2) KE = ½ (578 000 kg m2/s2 ) KE = 289 000 Nm or Joules, J

If the mass is doubled, KE will also doubled.

(velocity remains the same)

Example 1A 1000 kg car has a velocity of 34 m/s. What is the car’s kinetic energy?KE = ½ mv2

KE = ½ (1000 kg)(34 m/s)2

KE = ½ (1000 kg)(34 m/s)2

KE = ½ (1000 kg)(1156 m2/s2) KE = ½ (1 156 000 kg m2/s2 ) KE = 578 000 Nm or Joules, J

If the velocity is doubled, KE will be quadrupled.

(If mass remains the same)

Example 2A 1500 kg car has a velocity of 14 m/s. What is the car’s kinetic energy?KE = ½ mv2

KE = ½ (1500 kg)(14 m/s)2

KE = ½ (1500 kg)(14 m/s)2

KE = ½ (1500 kg)(196 m2/s2) KE = ½ (294 000 kg m2/s2 ) KE = 147 000 Nm or Joules, J

Example 2A 1200 kg car has a velocity of 10 m/s. What is the car’s kinetic energy?KE = ½ mv2

KE = ½ (1200 kg)(10 m/s)2

KE = ½ (1200 kg)(10 m/s)2

KE = ½ (1200 kg)(100 m2/s2) KE = ½ 120 000( kg m2/s2 ) KE = 60 000 Nm or Joules, J

Without computing if the velocity is constant, and the mass is doubled, what will be its KE?, if the mass is constant and the velocity is doubled, what will be its KE?

KE = 60 000 Nm or Joules, JIf the mass is doubled, KE will also be doubled, 60 000 J will become 120 000 J.If the velocity is doubled, KE will be quadrupled, 60 000 J will become 240 000 J.

A man lifting a box to be placed in the table

Potential Energy

Which/who is doing work in the illustration? Is it the table, the box, or the man?

Yes you are correct if you answer “The man is doing work on the box.”

What is the direction of the force exerted by the man on the box?

Yes, it is upward.

What is the direction of the motion of the box?

Yes, it is upward.

Then we can say, work is done by the man on the box.

As discussed previously, work is a way of transferring energy. Since the work is done by the man, he loses energy. The work is done on the box, hence the box gains energy.

In Grade 6, you learned about the force of gravity. It is the force that the earth exerts on all objects on its surface. It is always directed downward or towards the center of the earth. Hence, when an object is lifted from the ground, the work done is against the force of gravity.

An object gains energy when raised from the ground and loses energy when made to fall. The energy gained or lost by the object is called gravitational potential energy or simply potential energy (PE).

For example when a 1.0 kg book is lifted 0.5 m from the table, the force exerted in lifting the book is equal to its weight.

F=weight=mgThe acceleration due to gravity, g is

equal to 9.8 meters per second squared. The work done in lifting the book is

W=Fdwhere the displacement (d) is the height (h) to which the object is lifted.

W=mgh

This shows that the work done in lifting an object is equal to the potential energy gained by the object. The potential energy of the book lifted at 0.5 m relative to the table is:

PE=mghPE= 1kg (9.8 m/s2)0.5 mPE= 4.9 J

If the book is lifted higher than 0.5 m from the table, what would happen to its potential energy?

The potential energy gained and lost by an object is dependent on the reference level.

floor

book

.5 m1m

1m

table

chair

If the same 1.0 kg book is held 1 m above the table, the potential energy gained by it is 9.8 J with the table as the reference level; it is 14.7 J if the reference level were the chair; and 19.6 J if the reference level were the floor.

PE=mghPE= 1 kg (9.8 m/s2)(1m)PE= 9.8 J

PE=mghPE= 1 kg (9.8m/s2)(1.5m)PE= 14.7 J

PE=mghPE= 1 kg (9.8 m/s2)(2m)PE= 19.6 J

If the book is released from a height of 2 m, the potential energy lost when it reaches the level of the table top is 9.8 J; 14.7 J when it reaches the level of the chair; and 19.6 J when it reaches the floor.

ExampleIf the same 1.0 kg book is lifted to 0.5 m above the table, but the table top is 1.0 m above the floor, what would be the potential energy of the book if the reference level were the floor?

PE=mghPE= 1 kg (9.8m/s2)(1.5m)PE= 14.7 J

ExampleIf a book 3 kg mass is lifted 5 m above the floor, what would be the potential energy of the book if the reference level were the floor?

PE=mghPE= 3 kg (9.8m/s2)(5m)PE= 147 J

ExampleIf a book 3 kg mass is lifted 6 m above the floor, what would be the potential energy of the book if the reference level were the floor?

PE=mghPE= 3 kg (9.8m/s2)(6m)PE= 176.4 J

ExampleIf a book 3 kg mass is lifted 7 m above the floor, what would be the potential energy of the book if the reference level were the floor?

PE=mghPE= 3 kg (9.8m/s2)(7m)PE= 205.8 J

The energy of an object above the ground is called potential energy because it is a ‘stored’ energy. It has the potential to do work once released.

Think of water held in a dam. It has potential energy. Once released, the water has the potential to move objects along its way. The potential energy of the water is transformed into kinetic energy.

Objective: After performing this activity, you should be able to explain

how a twisted rubber band can do work and relate the work done to potential energy. 32

Materials Needed: 1 clear plastic container with cover 1 rubber band 1 pc 3-cm round barbecue sticks 1 pc barbecue stick with sharp part cut masking tape

Activity 2 Rolling toy

Procedure: 1. Make a hole at the center of the cover and at the bottom of the

plastic container.

Figure 7. A plastic container with holes

2. Insert the rubber band into the hole at the bottom of the container. Insert in between the rubber band the 3-cm barbecue stick. Tape the barbecue stick to keep it in place.

Figure 8. Steps in inserting the 3-cm barbecue stick

3. Insert the other end of the rubber band into the hole in the cover. Insert a bead or a washer to the rubber band before inserting the long barbecue stick.

Figure 9. Steps in inserting the bead and the long barbecue stick

4. You just made a toy. Twist the rubber band by rotating the long barbecue stick.

Figure 10. Rotating the long barbecue stick 3. Insert the other end of the rubber band into the hole in the cover. Insert a bead or a washer to the rubber band before inserting the long barbecue stick.

5. Lay the toy on the floor. Observe it.

Figure 11. Finished toy

Q1. What happens to the toy? Q2. What kind of energy is

‘stored’ in the rubber band? Q3. What kind of energy does a

rolling toy have? Q4. What transformation of

energy happens in a rolling toy?

Work, Energy, and Power So far, we have

discussed the relationship between work and energy. Work is a way of transferring energy. Energy is the capacity to do work.

Work, Energy, and Power When work is done by

an object it loses energy and when work is done on an object it gains energy. Another concept related to work and energy is power.

Power is the rate of doing work or the rate of using energy. In equation,

Power = Work/TimePower = Energy/Time

The unit for power is joules per second. But maybe, you are more familiar with watts which is commonly used to measure power consumption of electrical devices.

The unit watt is named after James Watt who was a Scottish inventor and mechanical engineer known for his improvements on steam engine technology. The conversion of unit from joules per second to watts is:

1 watt = 1 joule/second

Activity 3 How POWER-ful am I?

Objective: After performing this activity, you

should be able to compute for your power output in walking or running up a flight of stairs.

Materials Needed: meterstick Timer

Activity 3 How POWER-ful am I?

Procedure: 1. Write the group members’ names in the

first column of Table 1. 2. Enter each member’s weight in column 2.

To solve for the weight, multiply the mass (in kg) by acceleration due to gravity (g=9.8 m/s2).

3. Measure the height of the flight of stairs that you will climb. Record it on the table.

h

4. Each member will walk or run up the flight of stairs. Use a stopwatch or any watch to get the time it takes for each member to climb the stairs. Record the time in the 4th column.

5. Solve for the energy expended by each member. Record them in the 5th column of the table.

6. Compute for the power output of each member.

Name Weight (N) Height of stairs (m)

Time taken to climb the

stairs (s)

Energy expended

(J)

Power (J/s)

Q1. Who among the group members had the highest power output?

Q2. What is the highest power output?

Q3. Who among the group members had the lowest power output?

Q4. What is the lowest power output?

Q5. What can you say about the work done by each member of the group? Did each member perform the same amount of work in climbing the stairs?

Q6. What factor/s determined the highest/lowest power output?

These are the concepts that you need to remember about work and energy: • Work is done on an object when the

force applied to it covers a distance in the direction of the applied force. • Work is a way of transferring energy. • When work is done by an object it

loses energy and when work is done on an object it gains energy.

• The energy of an object enables it to do work. • A moving object has energy called energy of

motion or kinetic energy. • An object above a specified level has energy due

to its position called potential energy. • An elastic object that is stretched or compressed

or twisted has energy called potential energy. • Power is the rate of doing work or the rate of

using energy.

Prepared by:

Mr. Raymond S. ManalastasSST-I Mandili High School, Pampanga