Unit 1 module 2 work and energy

Unit 1 MODULE 2
WORK 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.

Unit 1 module 2 work and energy

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.

REVIEW
WORK IS DONE OR NO WORK IS
DONE
1. 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 WORK
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.

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

UNIT FOR WORK
W= Fd
Unit of work = unit of force x unit of displacement
Unit 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 = Fd
W = 500 N (7m)
W = 3500 Nm
W = 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 = Fd
W = 25 N (400 m)
W = 10 000 Nm
W = 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 = Fd
W = mgh
W = 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 = Fd
W = 500 N (5 m)
W = 2500 Nm
W = 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 = Fd
W = 15 N (4 m)
W = 60 Nm
W = 60 J

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

W = Fd
W = 50 N (3 m)
W = 150 Nm
W = 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 velocity
unit 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 1
A 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 1
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 )

If the mass is
doubled, KE will
also doubled.
(velocity remains the
same)

Example 1
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 )

If the velocity is
doubled, KE will
be quadrupled.
(If mass remains
the same)

Example 2
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 )

Example 2
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 )

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?

If 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=mg
The acceleration due to gravity, g is equal
to 9.8 meters per second squared. The work
done in lifting the book is
W=Fd
where 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=mgh
PE= 1kg (9.8 m/s2)0.5 m
PE= 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 m
1m
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=mgh
PE= 1 kg (9.8 m/s2)(1m)
PE= 9.8 J

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

PE=mgh
PE= 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.

Example
If 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?

Example
If 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=mgh
PE= 3 kg (9.8m/s2)(5m)
PE= 147 J

Example
floor?

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

Example
floor?

PE=mgh
PE= 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/Time
Power = 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:

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.

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.

Unit 1 module 2 work and energy

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Unit 1 module 2 work and energy