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2.10 UNDERSTADING WORK, ENERGY, POWER AND EFFICIENCY
Learning Outcome Define work(W) as W = Fs State that when work is done, energy is transferred
from one object to another. Define kinetic energy , Ek= ½ mv2
Define gravitational potential energy, Ey= mgh
WORK DONEWork is done in each of these situations.
What common characteristics can you observed?
A force is applied and the object moves through a distance in the direction of the force.
Work is defined as the product of the applied force and the displacement of an object in the direction of the applied force.
Work done = Force x displacement in the direction of the force.
DEFINATION OF WORK
where W = work done F = force s = displacement in the direction of force
W = F x s
Worked Example 1
If the car is pushed with a force of 3000 N and it moves through a distance of 0.5 m , calculate the work done.
Solution
Work done = F x s in the direction of force = 3000 x 0.5
= 1500 J Nm = J
Worked Example 2
The man lift a box of mass 8 kg through a height of 3 m. What is the work done by the man ?
Solution
Work done = F x s in the direction of force = 80 x 3
= 240 J
Disp. and force to lift the weight are in the same
directrion
The component of the force in the direction of the displacement is used to calculate the work done.
Work done = F x s in the direction of force = ( F cos )x s
OBJECT DOES NOT MOVE IN THE
DIRECTION OF THE APPLIED FORCE
F
F
s
F cos
F sin
Worked Example 3 pg 59
A woman pulls a suitcase with a force of 25 N at an angle of 60o with the horizontal.
Solution
Horizontal component of force = 25 cos 60o
Work done = F x s in the direction of force
= ( 25 cos 60o ) x 8
= 12.5 x 8
= 100J
What is the work done by the woman if the suitcase moves a distance of 8 m along the floor ?
No work doneNo work is done when A force is applied but no
displacement occurs, An object undergoes a
displacement with no applied force acting on it.
The direction of motion is perpendicular to the applied force.
Work done = force x displacement in the direction of force
Walking a few steps forward
Moves with constant velocity without any force
Reading
Think it overDetermine whether work is done
in each of the situations below
Pushing a car Pulling a locked door
Climbing up a ladder
Boxes are pushed up a
ramp
Waiting
Orbiting in spaceCarrying food and walking
Pulling a crate
Pushing a patient
Carrying begs of cement
X
X
X X
X
Chemical energy
kinetic energy
A librarian pushing a trolley of books
A bow is drawn
Chemical energy
Elastic potential energy
Chemical energy
Gravitational potential energy
Climbing up a flight of stairs
Weight lifting
Chemical energy
Gravitational potential energy
ENERGY TRANSFER (When work is done)
KINETIC ENERGY Kinetic energy is the energy of an object
due to its motion. Kinetic energy is given by Ek = ½ mv2
Example
What is the kinetic energy of a man of mass 50 kg jogging at a velocity of 4 m s-1 ?
solution
Ek = ½ mv2
= ½ (50)(4)2
= 400 J
m=massv=velocity
GRAVITATIONAL POTENTIAL ENERGY
Gravitational potential energy is the energy of an object due to its higher position in the gravitational field.
Gravitational potential energy is given by Ep = mgh
Example
solution Ep = mgh = (1.5)(10)(2.7) = 40.5 J
The mass of the basketball is 1.5 kg. What is the gravitational potential energy when it is 2.7 m above the ground ?
m=mass, h=heighg= acc due to gravity
ELASTIC POTENTIAL ENERGY Elastic potential energy is the energy of an object
due to its state of compression or extension. Elastic potential energy is given by Ee= ½ Fx or
Ee= ½ kx2
Example
solution Ee = ½ Fx = ½ (10)(0.12) = 0.6 J
F= forcex = extension
k = Force constantx = extension
The boy uses a force of 10 N to extend the elastic cord of the catapult by 12 cm. Calculate the elastic potential energy stored in the elastic cord.
Exercise
Mastery Practice 2.10 pg 65
Questions : 1, 2, 3
2.10 UNDERSTADING WORK, ENERGY, POWER AND EFFICIENCY
Learning Outcome State the principle of conservation of energy Define power and state that P = W/t Explain what efficiency of a device is Solve problems involving work, energy, power and efficiency.
Gravitational potential energykinetic energy
Water fall from a height
Gravitational potential energy
A gymnast bounces on a trampoline
kinetic energyElastic potential energy
Arrow is released from the bow
Elastic potential energy
kinetic energy
Gravitational potential energy
kinetic energyGravitational potential energy
A roller coaster
ENERGY TRANSFER(From one form to another)
PRINCIPLE OF CONSERVATION OF ENERGY
The principle of conservation of energy states that energy can be transferred from one form to another , but it cannot be created or destroyed.
Total amount of energy always remains the same.
A durian falls from a height of 20 m. What is the velocity of the durian just before it hits the ground ?
Worked Example 4( Exploring pg 127)
Solution
Gravitational potential energy is transformed to kinetic energy.
mgh = ½ mv2
m(10) 20 = ½ mv2
200 m = ½ mv2
v2 = 400
v = 400 = 20 m s-1
In a softball game, a ball was miss hit and flew vertically upwards with an initial velocity of 15 m s-1. What is the maximum height attained by the ball ? (Assume g= 10 m s-2)
Worked Example 5
Solution
Kinetic energy is transformed to gravitational potential energy.
½ mv2 = mgh
½ m(15)2 = m(10)(h)
112.5 = 10h
h = 11.25 m
A bow is extended 0.3 m by applying a force of 45 N. When the bow is released, the arrow shoots out with a velocity 2 m s-1. What is the mass of the arrow ?
Worked Example 6
Solution
Elastic potential energy is transformed to kinetic energy.
½ Fx = ½ mv2
½ (45)(0.3) = ½ m(2)2
m = 3.375 kg
POWER
When the weight is lifted quickly, the power generated is higher.
When the weight is lifted slowly, the power generated is lower.
Same work done
Power is defined as the rate at which work is done
Power = work done Time taken
P = W T
1 W = 1 J of work is done in 1 s
Worked Example 6 pg 63
A weightlifter lifts 160 kg of weights from the floor to a height of 2 m above his head in a time of 0.8 s. What is the power generated by the weightlifter during this time ? (g = 10 m s-2)
Solution
Work done , W = F x s
= 1600 x 2 = 3200 J
Power = W = 3200 = 4000 W t 0.8
Worked Example 7
A boy with mass 60 kg climbs up a flight of 20 stairs in 15 s. If the height of each stair is 0.18 m, what is the power generated by the boy ?
Solution
Work done , W = F x s
= 600 x (20 x 0.18) = 2160 J
Power = W = 2160 = 144 W t 15
EFFICIENCY
Not all the energy given is transformed into useful energy.
Some energy is transformed into unwanted energy and is wasted.
energy output is always less than
energy input
Efficiency is defined as the percentage of the energy input that is transformed into useful energy
Efficiency = useful energy output x 100% Energy input
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