CHAPTER
Work and Energy Perfect Your Physics
WORK AND ENERGY
4
LEARNING OBJECTIVES
At the end of this chapter the students will be able to:
1. Understand the concept of work in terms of product of force and displacement in the
direction of the force.
2. Understand and derive the formula Work = mgh for work done in a gravitational field
near Earth's surface.
3. Understand that work can be calculated from area under the force displacement
graph.
4. Relate power to work done.
5. Define power as the product of force and velocity.
6. Quote examples of power from everyday life.
7. Explain the two types of mechanical energy.
8. Understand the work-energy principle.
9. Derive an expression for absolute potential energy.
10. Define escape velocity.
11. Understand that in resistive medium loss of potential energy of a body is equal to
gain in kinetic energy of the body plus work done by the body against friction.
12. Give examples of conservation of energies from everyday life.
13. Describe some non-conventional sources of energy.
1 of 48
, G.F as Conservative Field
Exam Perspective : S.Q & MCQs Exam Perspective : L.Q, S.Q & MCQs Exam Perspective : S.Q, MCQs &
Work and Energy
L.Q (Important)
Power & Velocity
Energy from waves & Tides
Solar & Geothermal Energy
2 of 48
Energy from waste products
Exam Perspective : MCQs & S.Q Exam Perspective : S.Q & MCQs
Kinetic & Potential Energy
Law of Conservation of Energy
Work-Energy Principle
Absolute P.E
Exam Perspective : MCQs & S.Q Exam Perspective : S.Q, MCQs & Exam Perspective : S.Q, MCQs &
L.Q (Important) L.Q
Perfect Your Physics
,Work and Energy Perfect Your Physics
4.1 WORK DONE BY A CONSTANT FORCE
Question:
Define the term work? How work is done by constant force? Explain with examples.
RELATED QUESTIONS
Define Work, write its formula if force is constant.
When does work done is positive and when does it is negative? Explain.
write the formula for work. How it is found by Fd-graph?
Give example of Zero work.
Give examples of positive and negative work.
Describe the circumstances in which work done is negative and no work is done even in
presence of applied force.
(FSD 2015)
Answer:
Work Done By Constant Force:
“The work done on a body by a constant force is defined as the
product of the magnitudes of displacement and the component
of the force in the direction of the displacement.”
OR
“When force is applied and body gets some displacement in the
direction of force then work is said to be done which is equal to
the product of component of force in direction of displacement
and magnitude of displacement.”
Explanation:
Consider an object which is being pulled by a constant force F at an
angle θ to the direction of motion. The force moves the object from
position A to B through a displacement d .
The work done by the force is defined as the scalar product of F
and d
W= F . d =Fdcosθ
W= Fcosθ d..................(i)
FCosθ = the component of force in the direction of displacement.
Eq. (i) may be writtem as
Work = Fd cos = F . d
Thus, work is also defined as the dot product of force and displacement.
Examples of Work:
(i) Work Done on the Pail:
If a person holding the pail in his hand walks, no work is done
because the angle between force and displacement is 90o.
As W = Fd cos = Fd cos 90o = 0
W=0 ( cos 90o = 0)
3 of 48
, Work and Energy Perfect Your Physics
(ii) Work Done on the Wall:
When a man pushes a wall it does not move. It means displacement of the wall is zero.
W = Fdcos=F(0) cos = 0
W=0
Work Done By Graphical Method
When a constant force acts a body and body covers a distance d. The
event can be plotted in a graph. The distance is taken along x-axis
and force is taken along y-axis. In this case the graph will be a
horizontal straight line. There are two cases
i. If force and displacement are in the same direction, we plot a
graph between F and d.
ii. If force makes an angle θ with the displacement, we plot a graph
between Fcos θ and d.
The work done by a force can be calculated by calculating the area
under F d curve as
Area=OP×OR=Fd
Area=OQ×OR= Fcosθ ×d
Area=work
S I unit of work:
S I unit of work is Joule which is defined as.
Joule:
The work done is said to be one joule if one Newton force acts on a body and the body covers
a displacement of one meter in the direction of force.
OR
If the force of 1 newton’s is acting on the body and the body covers the distance of 1m in the
direction of force then work done is said to be one joule.
That is For Your Information
1 joule = 1N 1m.
It is represented by 1 erg = 10-7 J
Note: The unit of work in CGS is Erg and is FPS is 1 ft- b = 1.3105 J
foot lb.
Dimension of work:
Work = Force displacement.
Joule = Newton Meter.
J = kg m/s2 m.
= kg m2/s2
[J] =
M L2
[T2 ]
Dimension of work = [ML2T-2]
Special Cases of work done
There are some special cases that can be derived from the definition of work, these are
(i) Positive Work:
When the angle between the force and displacement is less than 90o i.e. < 90o then positive
work is said to be done.
Also, when the force and displacement are in same direction or when = 00, the positive
maximum work is said to be done.
4 of 48
Work and Energy Perfect Your Physics
WORK AND ENERGY
4
LEARNING OBJECTIVES
At the end of this chapter the students will be able to:
1. Understand the concept of work in terms of product of force and displacement in the
direction of the force.
2. Understand and derive the formula Work = mgh for work done in a gravitational field
near Earth's surface.
3. Understand that work can be calculated from area under the force displacement
graph.
4. Relate power to work done.
5. Define power as the product of force and velocity.
6. Quote examples of power from everyday life.
7. Explain the two types of mechanical energy.
8. Understand the work-energy principle.
9. Derive an expression for absolute potential energy.
10. Define escape velocity.
11. Understand that in resistive medium loss of potential energy of a body is equal to
gain in kinetic energy of the body plus work done by the body against friction.
12. Give examples of conservation of energies from everyday life.
13. Describe some non-conventional sources of energy.
1 of 48
, G.F as Conservative Field
Exam Perspective : S.Q & MCQs Exam Perspective : L.Q, S.Q & MCQs Exam Perspective : S.Q, MCQs &
Work and Energy
L.Q (Important)
Power & Velocity
Energy from waves & Tides
Solar & Geothermal Energy
2 of 48
Energy from waste products
Exam Perspective : MCQs & S.Q Exam Perspective : S.Q & MCQs
Kinetic & Potential Energy
Law of Conservation of Energy
Work-Energy Principle
Absolute P.E
Exam Perspective : MCQs & S.Q Exam Perspective : S.Q, MCQs & Exam Perspective : S.Q, MCQs &
L.Q (Important) L.Q
Perfect Your Physics
,Work and Energy Perfect Your Physics
4.1 WORK DONE BY A CONSTANT FORCE
Question:
Define the term work? How work is done by constant force? Explain with examples.
RELATED QUESTIONS
Define Work, write its formula if force is constant.
When does work done is positive and when does it is negative? Explain.
write the formula for work. How it is found by Fd-graph?
Give example of Zero work.
Give examples of positive and negative work.
Describe the circumstances in which work done is negative and no work is done even in
presence of applied force.
(FSD 2015)
Answer:
Work Done By Constant Force:
“The work done on a body by a constant force is defined as the
product of the magnitudes of displacement and the component
of the force in the direction of the displacement.”
OR
“When force is applied and body gets some displacement in the
direction of force then work is said to be done which is equal to
the product of component of force in direction of displacement
and magnitude of displacement.”
Explanation:
Consider an object which is being pulled by a constant force F at an
angle θ to the direction of motion. The force moves the object from
position A to B through a displacement d .
The work done by the force is defined as the scalar product of F
and d
W= F . d =Fdcosθ
W= Fcosθ d..................(i)
FCosθ = the component of force in the direction of displacement.
Eq. (i) may be writtem as
Work = Fd cos = F . d
Thus, work is also defined as the dot product of force and displacement.
Examples of Work:
(i) Work Done on the Pail:
If a person holding the pail in his hand walks, no work is done
because the angle between force and displacement is 90o.
As W = Fd cos = Fd cos 90o = 0
W=0 ( cos 90o = 0)
3 of 48
, Work and Energy Perfect Your Physics
(ii) Work Done on the Wall:
When a man pushes a wall it does not move. It means displacement of the wall is zero.
W = Fdcos=F(0) cos = 0
W=0
Work Done By Graphical Method
When a constant force acts a body and body covers a distance d. The
event can be plotted in a graph. The distance is taken along x-axis
and force is taken along y-axis. In this case the graph will be a
horizontal straight line. There are two cases
i. If force and displacement are in the same direction, we plot a
graph between F and d.
ii. If force makes an angle θ with the displacement, we plot a graph
between Fcos θ and d.
The work done by a force can be calculated by calculating the area
under F d curve as
Area=OP×OR=Fd
Area=OQ×OR= Fcosθ ×d
Area=work
S I unit of work:
S I unit of work is Joule which is defined as.
Joule:
The work done is said to be one joule if one Newton force acts on a body and the body covers
a displacement of one meter in the direction of force.
OR
If the force of 1 newton’s is acting on the body and the body covers the distance of 1m in the
direction of force then work done is said to be one joule.
That is For Your Information
1 joule = 1N 1m.
It is represented by 1 erg = 10-7 J
Note: The unit of work in CGS is Erg and is FPS is 1 ft- b = 1.3105 J
foot lb.
Dimension of work:
Work = Force displacement.
Joule = Newton Meter.
J = kg m/s2 m.
= kg m2/s2
[J] =
M L2
[T2 ]
Dimension of work = [ML2T-2]
Special Cases of work done
There are some special cases that can be derived from the definition of work, these are
(i) Positive Work:
When the angle between the force and displacement is less than 90o i.e. < 90o then positive
work is said to be done.
Also, when the force and displacement are in same direction or when = 00, the positive
maximum work is said to be done.
4 of 48
