2. The product of the displacement and the component of the
force in the direction of the displacement is called work.
W = (F cos) (d)
Positive Work
For < 90º, work done is positive.
Maximum positive work is done if = 0º
Example when an engine pulls a train.
WORK
3. Zero work
Work will be zero
when = 90º,e.g.centripetal force and tension in
pendulum string does not do any work
when F=0, e.g: boy exerts force on a wall.
When 𝑑 = 0, e.g: car is not moving while its engine is
running.
Negative Work
For >90º, work done is negative.
Maximum negative work when = 180º
Example: work done by frictional forces
4. = 0o Wmax = Fd
= 30o W = 86% Wmax
= 45o W = 70% Wmax
= 60o W = 50% Wmax
In S.I the unit of work is joule (J) and in C.G.S
the unit of work is erg.
Graphically work can be obtained from force
displacement graph.
Work done = Area of rectangle = (OA) (AB) = (F) (d)
Work Done by a Variable Force:
Work done =
n
i i i
d 0 i=1
lim Fcosθ Δd
5. Conservative Field:
If a field satisfies following two conditions, it is said to be conservative.
Work done along a closed path is zero i.e. Wtotal = 0
Work done is independent of path followed by body but depends on final
and initial position of a body.
Example: Electric field, Gravitational field.
Example of Non-conservative force:
Frictional force, propulsion force on rocket, force of a motor, tension in
string etc.
Conservative field and conservative force has the property of storing
energy in the system. This energy is known as P.E of the system.
6. It is ability to do work.
The SI unit of energy is joule. Other units of energy are erg,
foot-pound and kilowatt-hour etc.
Types of Energy: mechanical, electrical, chemical, nuclear,
magnetic, heat and elastic energy etc.
Mechanical energy are of two types: Kinetic energy and
Potential energy.
ENERGY
7. Kinetic Energy
𝐾. 𝐸 =
1
2
𝑚𝑣2
=
1
2
𝑚 𝑣. 𝑣 =
1
2
pv =
𝑝2
2m
𝑝 = 2𝑚𝐾. 𝐸
For two bodies having equal momentum
𝐾.𝐸1
𝐾.𝐸2
=
𝑚2
𝑚1
For two bodies having equal kinetic energies:
𝑝1
𝑝2
=
𝑚1
𝑚2
KINETIC ENERGY
8. The energy possesses by the body by virtue of its position is
called P.E
Gravitational Potential Energy of a body of mass m at height h
from surface of earth: 𝑃. 𝐸 = 𝑚𝑔ℎ
P.Eg = U = −
GMm
𝑟
GRAVITATIONAL POTENTIAL ENERGY
9. 𝑃 =
𝑊
𝑡
𝑃 = 𝐹. 𝑣 or, P = Fv cos
P= 𝑙𝑖𝑚
𝛥𝑡→0
ΔW
Δt
.
𝑃 = 𝜏. 𝜔
If <P> = Pins, then body does work at constant rate.
Unit of power is watt defined as; 1 W = 1 J/1 sec
1 hp = 746 watt = 550 foot pound/sec
POWER
10. Work done = Change in kinetic energy = K.Ef – K.Ei or
𝑾 =
𝟏
𝟐
𝒎𝒗𝒇
𝟐
−
𝟏
𝟐
𝒎𝒗𝒊
𝟐
If a car stopped by applying brakes, then the stopping
distance
𝑠 =
𝑚𝑣2
2𝐹
⇒ 𝑠 ∝ 𝑣2
WORK ENERGY PRINCIPLE
11. WORK DONE AGAINST FRICTION IS DISSIPATED AS HEAT IN
THE ENVIRONMENT
Conservation of Energy
Energy cannot be destroyed. It can be transformed from
one form into another, but total amount of energy remains
constant.
12. In absence of air, then;
Loss in P.E. = Gain in K.E.
𝑚𝑔 ℎ1 − ℎ2 =
1
2
𝑚 𝑣2
2
− 𝑣1
2
In presence of air, then;
Loss in P.E = gain in K.E + work done against air.
𝑚𝑔ℎ =
1
2
𝑚𝑣2
+ 𝑓ℎ
If a body is thrown vertically upward in gravitational field
Loss in K.E = gain in P.E + work done against air.
1
2
𝑚𝑣2
= 𝑚𝑔ℎ + 𝑓ℎ
13. Mechanical efficiency is the ratio of work output to work
input.
The efficiency of an ideal machine is 100 percent but an
actual machine’s efficiency will always be less than 100%.
Output = Load x distance h through which the load
moves
= 𝑭𝒐𝒖𝒕 × 𝑫𝒐𝒖𝒕
In put= Effort force x Effort distance.
In put= FinxDin
IMPLICATIONS OF ENERGY LOSSES IN PRACTICAL DEVICES
Output work
Percentage Efficiency= 100% 100%
Input work
100%
out
in
out out
in in
W
W
F D
F D
14. A force of 10N is acting on an object at angle of 120°
through a distance of 4m. Calculate the work done.
(a) –20 J
(b) 20 J
(c) 40 J
(d) –40 J
QUESTION-1
15. The work done by force “𝑭” in figure shown is
(a) Fd cos
(b) Fd sin
(c) Fd tan
(d) Fd cot
QUESTION-2
16. When work done by the gravity is positive then P.E of the
body
(a) Increases
(b) Decreases
(c) Remains same
(d) Can’t be predicted
QUESTION-3
17. A brick of mass 2kg falls from height 10m. Find its
velocity when its height is 5m
(a) 10ms–1
(b) 5ms–1
(c) 2ms–1
(d) 15ms–1
QUESTION-4
18. Two bodies with kinetic energies in the ratio of 4 : 1 are
moving with equal linear momentum. The ratio of their
masses is:
(a) 1 : 2
(b) 1 : 1
(c) 4 : 1
(d) 1: 4
QUESTION-5
19. A body of mass 5kg, initially at rest, is moved by a
horizontal force 2N. Find word done by force in 10s.
(a) 40J
(b) 30J
(c) 20J
(d) 10J
QUESTION-6
20. Efficiency of motor is 20%. It takes 4s to take a load of
100N upto height 80cm. Find power input
(a) 60W
(b) 50W
(c) 90W
(d) 100W
QUESTION-7
21. If a certain force acts on an object and changes its kinetic
energy from 65 J to 130 J, then work done by the force
will be:
A. 92.5 J
B. 65J
C. 97.5 J
D. 130 J
QUESTION-8
22. An engine pumps out 40 kg of water in one second. The
water comes out vertically upwards with a velocity of
3ms–1, the power of engine in kilowatt is:
A. 1.2 kW
B. 12 kW
C. 120 kW
D. 1200 kW
QUESTION-9
