Download force and motion

2.10 : WORK, ENERGY, POWER AND EFFICIENCY
WORK
Is defined as the product of the applied
force and the distance moved in the
direction of the force.
 Work = force x distance
W=Fxs
 SI unit is the Joule (J)
 Is a scalar quantity

No work done when:
1.
A force is applied but no displacement
occurs.
2.
An object undergoes a displacement
with no applied force acting on it.
3.
The direction of motion is perpendicular
to the applied force.
3 SITUATION THAT INVOLVE
WORK
1.
Direction of force, F is same as the
direction of displacement, s.
F
F
s
W=Fxs
2.
Direction of force, F is not same as the
direction of displacement, s.
F
F
θ
θ
s
W = F cos θ x s
W = F s cos θ
F cos θ
3.
Direction of force, F is perpendicular to
the direction of displacement, s.
F
F
s
W=Fxs
W = F cos 90° x s
W=0
Example 1
If a box is pushed with a force of 40 N
and it moves steadily through a
distance of 3m in the direction of the
force, calculate the work done.

Answer: W = 120 J
Example 2
A women pulls a suitcase with a force of
25 N at an angle of 60° with the
horizontal. What is the work done by the
women if the suitcase moves a distance
of 8 m along the floor?

Answer,: W = 100 J
FORCE–DISTANCE GRAPH

Area under a force–distance graph =
work done.
Force, F
a
b
Distance, s
Work = F x s
=axb
WORK DONE AGAINST THE
FORCE OF GRAVITY

An upward force, F is applied to lift the
object of weight, W to a height, h.

W=Fxh
F

W = mgh
h
W
ENERGY
Is defined as potential or the ability to do
work.
 Form energy:

 Gravitational potential energy
 Kinetic energy
 Heat energy
 Sound energy
 Electrical energy
SI unit in Joule, J and it scalar quantity.
 Energy is transferred from 1 object to
another when work is done.

KINETIC ENERGY, Ek
Is a energy possessed by a moving
object.
 It scalar quantity.
 SI unit in Joules, J.
 Formula :

 Ek = 1 mv2
2
 Ek = 1(mv2) – 1(mu2)
2
2
Object moving from initial
velocity to final velocity
POTENTIAL ENERGY, Ep
Defined as energy of an object due to its
higher position in the gravitational field.
 Depend on mass, gravitational field and
height.
 Formula:

 Ep = mgh
# m = mass
# g = acceleration due to gravity
# h = difference between height
Example 3
In a school sports event, a student of
mass 40 kg runs past the finishing line
with a velocity of 7 ms-1. Calculate his
kinetic energy.

Answer: Ek = 980 J
Example 4
A durian fruit hanging from its branch
has gravitational potential energy due to
its higher position above the ground.
The mass of the fruit is 2.5 kg and it
hangs 3 m above the ground. What is
the gravitational potential energy of the
fruit? (g = 10 ms-2)
Answer: Ep = 75 J
PRINCIPLE OF CONSERVATION
OF ENERGY
State that energy cannot be created or
destroyed.
 It can be transformed from one form to
another.
 The total energy in a system is constant.
This means there is no energy gained or
lost in a process.
 Formula :

mgh = 1mv2
2
Example:

On winning a match, a tennis player hits
a tennis ball vertically upward with an
initial velocity of 25ms-1. What is the
maximum height attained by the ball? (g
= 10ms-2)

Answer ;
 h = 31.25 m
POWER
Is the rate at which work is done or rate at
which energy is transformed.
 Formula;
Power, P = work done @ energy transformed
time taken
time taken
P = W @ F x s @ F x s @ Fv
t
t
t
P ∞ W if t constant
P=E
P ∞ 1 / t if work constant
t
 SI unit is watt (W) or Js-1
 Is scalar quantity

Example:

A weightlifter lifts 160kg of weights from
the floor to a height of 2m above his
head in a time of 0.8s. What is the
power generated by the weightlifter
during this time? (g = 10ms-2)

Answer :
 P = 4000 W
EFFICIENCY
The percentage of the input energy that is
transformed to useful form of output energy.
 Formula :
efficiency = useful energy output x 100%
energy input
= Eo x 100%
Ei


Also can be calculated in terms of
power.
efficiency = useful power output x 100%
power input
= Po x 100%
Pi
Example:

a.
b.

a.
b.
An electric motor in a toy crane can lift a
0.12 kg weight through a height of 0.4m
in 5s. During this time, the batteries
supply 0.80 J of energy to the motor.
Calculate
The useful energy output of the motor
The efficiency of the motor
Answer:
Eo = 0.48J
Efficiency = 60 %
Exercise
1.
A steel ball of mass 2 kg is released from a height of 8 m
from the ground. On hitting the ground, the ball rebounds to a
height of 3.2 m as shown in figure.
8m
a.
b.
c.
d.
3.2 m
If air resistance can be neglected and the acceleration due to
gravity g = 10 ms-2, find
The kinetic energy of the ball before it reaches the ground.
The velocity of the ball on reaching the ground.
The kinetic energy of the ball as it leaves the ground on
rebound.
a. Ek =160 J
The velocity of the ball on rebound.
b. v1 = 12.65 ms-1
c. Ek = 64 J
d. v2 = 8 ms-1
Exercise
A car moves at a constant velocity of 72
kmj-1. Find the power generated by the
car if the force of friction that acts on it
is 1500 N.
Answer :
2.


P = 30000 W