2.10 work, power, efficiency

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