WORK, ENERGY,

POWER
Physics I
LESSONS:
I. Work
II. Energy
III. Total Mechanical Energy
IV. Work-Energy Theorem
V. Laws of Conservation of Energy
VI. Power
WHICH AGENT CAUSES OR TENDS
TO CAUSE MOTION IN A BODY?

- It is the “force” which causes

or tends to cause motion in a
body.
WHAT IS FORCE ?

The agent which:

Stops or tends to stop the motion; or
Produces or tends to produce the motion
WHICH PATH IS THE
SHORTEST IN THE FIGURE
SHOWN?

 Displacement
WHICH QUANTITY DEPENDS
UPON FORCE AND
DISPLACEMENT?

 Work
WORK
I. Definition
II. Mathematical Form
III. Unit
IV. Cases of Work
WHAT IS WORK?
Work is said to be done when a force
acts on a body and moves it through a
certain displacement.
WORK: MATHEMATICAL FORM

If force F is applied on a body and it moves the body

through a displacement ‘d ’, then the work W is
defined by the relation:
W = F. d
WORK

W = F. d
What is the nature of work?
- Work is a scalar quantity.
WORK
If the force makes an angle θ with the
direction of the displacement then, take
the component of the force in the
direction of the displacement.
WORK: UNIT
The SI unit of work is joule (J).
One Joule
-When a force of one Newton moves a body
through a distance of one meter in the direction
of force, then the work done is equal to one
joule.
1J= 1N.1m
CASES OF WORK: POSITIVE WORK

When force and displacement are in the

same direction, then
θ = 0°
W = F d cos 0°
= Fd x1
= Fd
 In this case, work done is maximum and is
equal to the product of the magnitude of
force and displacement.
14
CASES OF WORK:
ZERO WORK
When force is perpendicular to the displacement
Then:
θ = 90°
W = F d cos 90°
= Fd x0
=0
In this case work done is zero.
CASES OF ZERO WORK:
EXAMPLE
CASES OF WORK: NEGATIVE WORK

When force and displacement are in the

opposite direction,
Then
θ = 180°
W = F d cos 180°
= F d x (-1) (cos 180° = -1)
W = -Fd
Recall
WHAT IS THE DEFINITION OF WORK?

It is the product of displacement and component of

force along displacement.

What is the unit of work?

 The unit of work is “Joule”.
Recall
GIVE AN EXAMPLE OF POSITIVE WORK
Pushing something horizontally is an example of positive work.

Give an example of negative work

 Lifting an object vertically upwards

Give an example of zero work

If a person holds the pail in his hand and walks along
a level surface.
 #1 SAMPLE PROBLEM

Given Data
Applied force = F = 300 N
Displacement covered by body = d = 10m
Angle between force and displacement = θ = 60o
Work done =w =?
 #2 SAMPLE PROBLEM

A bungee jumper has a weight of 700 N.

How much work has he done in jumping to
a height of 3 m. Express this value in
calories as well. (1 J= 4.186 cal)
ACTIVITY
IS WORK DONE?
Direction: Put a check before the item if work is done on the
following situations. Otherwise, put an x mark.
 1. Pushing a wall
 2. Lifting a suitcase
 3. A waitress carrying a tray full of meals above her head
by one arm and walks inside the room
 4. Pushing a large crate along the ground from one place
to another
 5. Holding a cellular phone
1. How much work 2. How much work 3. A cartload of sand is pulled 5
do you do by is done by a student m across the ground as shown
pushing a sack of who lifts a 5-kg box below. The tension in the rope is
rice with a force of to a vertical height 300 N and is directed 30 degrees
100 N across a of 1.5 m? above the horizontal. How
distance of five GIVEN & UNKNOWN: much work is done in pulling
 
meters?   the load?
GIVEN & UNKNOWN:
 
FORMULA:
SOLUTION & ANSWER:
“
  Note: The force required to lift   “

FORMULA: the box is equal to the weight  

SOLUTION & ANSWER: of the box, which is the 5m
  product of the mass and GIVEN & UNKNOWN:
  acceleration due to gravity.  
  That is, F = mg  
    FORMULA:
SOLUTION & ANSWER:
FORCE VS DISPLACEMENT
GRAPH
FORCE VS DISPLACEMENT
GRAPH
Presentation title 30
Presentation title 31
Presentation title 32
Presentation title 33
 34

ENERGY
Potential Energy
Kinetic Energy
Total Mechanical Energy
Work-Energy Theorem
 35

ENERGY
• When work is done, energy is transformed from one type to
another.
• Thermodynamics: the study of energy relationships,
transformations, and exchanges
• Energetics:
a. The one in the system
b. The other one in the environment or outside the system
Presentation title 36

POTENTIAL ENERGY

• Objects can have energy associated with their position,

nature, and/or arrangement of parts.
• 2 types: Potential Energy
Presentation title 37

POTENTIAL ENERGY

1. Gravitational Potential Energy

2. Elastic Potential Energy
Presentation title 38

1. GRAVITATIONAL POTENTIAL ENERGY

(GPE)

• Gravity acts as a force causing the conversion of potential

energy to kinetic energy.
• Example
• GPE = mgh
Presentation title 39

1. GRAVITATIONAL POTENTIAL ENERGY

(GPE)

Example: falling rock

 Mass
 Initial height
 Lower height
• Mass of the rock is acted upon by
gravitational force (Fg) = weight of the
object (Fg = mg = weight)
 Other forces
Presentation title 40

1. GRAVITATIONAL POTENTIAL ENERGY

(GPE)

• Fg and displacement of the object from

h1 to h2 are in the same direction =
positive work done
W = Fg d
W = (mg)(h1 - h2 )
W= mgh1 – mgh2
* Remember: GPE= mgh
 Presentation title 41

1. GRAVITATIONAL POTENTIAL ENERGY

(GPE)
• Remember: GPE= mgh
• Thus, a change in terms of GPE happens
when the stone falls from h1 to h2.
• This change in potential energy is related to
the work done by the gravitational force in
bringing the stone from h1 to h2.
W= mgh1 – mgh2
W= GPE1 - GPE2 = ∆GPE
 Presentation title 42

1. GRAVITATIONAL POTENTIAL ENERGY

(GPE)
W= mgh1 – mgh2
W= GPE1 - GPE2 = ∆GPE
 GPE is positive because the direction of
gravitational force and displacement of the object
are in the same direction.
When does GPE become negative?
 However, this change in GPE will be negative if the
stone is raised to higher position instead of letting
it fall, as the directions of the two vectors now
become opposite.
Presentation title 43

2. ELASTIC POTENTIAL ENERGY (EPE)

• Potential energy stored by deforming an elastic object

• Examples: spring, rubber band, muscles in the human body
A spring being pulled on the opposite ends. As work (the pull) is done on it, the
spring stretches. It will continue to be stretched out until it is released. The act of
pulling stores the EPE on the spring, which is converted to KE when it is released.
The spring then returns to its original shape if the force is not sufficient to deform the
spring.
Presentation title 44

2. ELASTIC POTENTIAL ENERGY (EPE)

Massless spring
• Consider a spring attached at one end and exert a force along
the x-axis to the opposite side. In order to maintain the
displacement, a constant force needs to be exerted:
F= kx
Presentation title 45

2. ELASTIC POTENTIAL ENERGY (EPE)

F= kx
k= spring constant
F= force
x= displacement along the x-axis

When the block is released, the block will move back and forth.
Determine the work done in moving the block from x1 to x2.

W= ½ kx
W= ½ - ½
EPE= ½ kx2
Presentation title 46

2. ELASTIC POTENTIAL ENERGY (EPE)

EPE= ½ kx2
Work done by the spring
WE = ½ - ½
= EPE1 – EPE2
WE = -∆EPE
Pattern for work done and the EPE for specific cases:
CASE WORK EPE
Stretched spring negative Increases
Relaxes spring after stretching positive decreases
 KINETIC ENERGY
Presentation title 47

• Energy that an object

possesses while in
motion
• KE= ½ mv2
Presentation title 48

TOTAL MECHANICAL ENERGY

(TME)
• The sum of the kinetic and potential energy
• Example: stone
TME= KE + PE
TME= ½ mv2 + mgh
Applying our idea of the TME, we get
½ mv21 + mgh1 = ½ mv22 + mgh2
TE1 = TE2
 CONSTANT
Presentation title 49

TOTAL MECHANICAL ENERGY

(TME)
• Another way to determine if the TME of an changes or remains
constant, is by identifying the type of force that displaces the object
 External Forces: applied, normal, tension, friction, air resistance forces
– TME changes
 Internal Forces: gravitational and spring forces – TME remains constant
- Even if there is transformation of energy in the object to do the work, the sum of
the PE and the KE does not change.
TME= GPE + KE = constant
TME= EPE + KE = constant
Presentation title 50

TME
EXAMPLES
• Roller Coaster Ride
• Dropped coin
Presentation title 51

TME
Presentation title 52

TME
Problem-Solving
- A wagon in a roller coaster starts at a maximum height of 60
m. If the mass of the passenger-filled wagon is 400 kg, what is
the total mechanical energy at any point on the path of the
roller coaster?
Presentation title 53

WORK-ENERGY THEOREM
• It states that: regardless of the increase and decrease in kinetic energy,
the change in energy equals the amount of work done on the object.
WTotal = ∆ KE
Presentation title 54

WORK-ENERGY THEOREM

• Force is exerted in the same direction as the initial direction of the

object’s motion.
WORK-ENERGY THEOREM 55
Presentation title 56

• Notice how the KINETIC ENERGY of the object changes, depending on the direction of the force and the
corresponding net force.
Presentation title 57

WORK-ENERGY THEOREM
• The units of work and energy can be deduced as the same.
• Joule (J), calorie (cal), and British thermal unit (Btu) can both be used
as unit indicators.
KE=
= 1 kg (
=1
KE= 1N•m or 1 J
Notice that: 1 cal = 4.186 J
1 Btu = 1055 J
Presentation title 58

SOLVING FOR WORK

BY USING POTENTIAL ENERGY
Presentation title 59

GRAPHICAL REPRESENTATION
 60

LAW OF CONSERVATION
OF ENERGY

THERMODYNAMICS:
STUDY OF NATURE OF HEAT, ITS TRANSPORT,
AND ITS EFFECTS
 61

LAW OF CONSERVATION OF ENERGY

(LCE)
• States that energy can be transformed or converted from one
form to another, but it cannot be created nor destroyed.
• It involves more than kinetic and potential energy, for it also
concerns internal energy (IE)
Presentation title 62

POWER
POWER
- The rate at which work is done
- Scalar quantity
- SI Unit: Watt
ASSIGNMENT: POWER
THERMODYNAMICS
PROCESSES
THANK YOU