PHYSICS CLASS: WORK ENERGY AND POWER

Work could be defined as the product of force and distance moved in the direction of the force. If a force “F” moves a body a distance “S” in the direction of the force the work one is given by

w = fxs

The sknit of work is joule

Work = force x displacement

(joules) = newtons x metres

WORK DONE IN A FIELD

A typical example of work done in a force field is the grantational field, to lift up a body under gravity e.g. lifting up a bucket of water; a force must be applied to overcome the weight of the body. The magnitude of this work done is

Force x distance

Mg x h

Work done = mgh

Where m = mass of the body (kg)

g = acceleration due to gravity

h = height

This also applies when a body falls from a high the work done = mgh

Simplified 21 if an engine of force 200µ pulls a train 100m what is the work done by the engine.

Solution

Work done = f x s

= 200 x 100

= 20,000

Simplified 22 A body of mass ran up a flight of 31 steps, each 15cm high calculate the work by the body (take g = 10m5^-2)

Solution

Mass = 70kg

S = 15cm convert to metres = 0.15m

This work is done due to gravity the

workdone =mgh

h = 31steps x 0.15

h = 4.65

w = 70x10x4.65

W = 3255

Simplified 23 the work done when an object is lifted through a vertical distance of 300cm is 450. Find the mass of the object.

Solution

Workdone = force x distance

W = mg x h

M =?, w = 450, h = 300cm = 3m

450 = mx10x3

450 = 30m

M = 450 = 15kg

CONCEPT OF ENERGY

Energy is defined as the capacity or ability to do work, energy is a scalar quantity and the 5.1 unit.

Joules

FORMS OF ENERGY

Solar energy

Nuclear energy

Chemical energy

Heat energy

Sound energy

Light energy

Mechanical energy

Electrical energy etc

MECHANICAL ENERGY

The two forms of mechanical energy we have are

Potential energy

Kinetic energy

POTENTIAL ENERGY: This is defined as the energy possessed by an object by virtue of its position. Potential energy has the same formula as workdone.

P. E = mgh

This type of potential energy is called grantational energy which is a measure of the amount of workdone in raising a body to its position.

However the potential energy possessed or stored by springs, elastic strings when stretched to a certain distance “e” is given by the equation.

Workdone = average force x extension.

= ½ fe

KINETIC ENERGY: This is energy which a body has by virtue of its motion.

K.E = 1/2MV²

Where m = mass of an object in kg

V = velocity in m51

NOTE (1) K. E = PE, K.E + P.E = constant

(2) Work, potential energy and kinetic energy are all related. The workdone of a given boy is either equal to the kinetic energy possessed by the body or it is equal to its potential energy

Simplified 24 an object of mass 5kg is moving at a constant velocity of 50m51 calculate its kinetic energy

Solution

K. E = ½ mv²

K.E = ½ x 5 x (50)²

K.E = ½ x 5x2,500 = 6,250

Simplified 25 an object of mass 4kg at 5m51 was brought to rest over a distance of 2.8m find the magnitude of the force that brought the object to rest.

Solution

Workdone = force x distance

Workdone =?

F = ?

D = 2.8

But K.E = workdone

K.E = ½ mv²

M = 4kg

V = 5m51

K. E = ½ x (4) x (5)² = 50J

K. E = work done byt K.E = 50

50 = f x d

50 = fx2.8

50 = F

f = 17.9µ

2.8

Simplified 26 A body of mass 5kg falls from a height of 10m above the ground. What is the kinetic energy of the body just before it strikes the ground (neglect energy lost and take g = 10m5²)

Solution

M = 50kg

H = 10m

V = ?

From equation of motion v² = u2 x 2gh

V² = 0x2x10x10

V² = 200

K.E = ½ MV²

= ½ x 5x200

= 500

Simplified 27 A stationary sledge of mass kg is acted on by a force of 8N for 5seconds calculate its kinetic energy.

Solution

K.E = 1/2MV² m = 4kg, f = 8µ,

= 5seconds from equations of motion

V = u +a

……… (i)

From newton’s first law of motion

F = ma

a = f/m = 8/4 = 2m5²

But a = 2m52 in equation (1)

v = 0 x 2 x 5 = 10m51

CONCEPT OF POWER

Power is defined as the rate of doing work (The rate of converting energy). Or power is workdone per time taken.

Average power = workdone or force x distance

time taken time taken

For power = force x velocity

Also f = mg

Where P = power in waste or J5¹

F = force in Newton (µ)

S = distance in metres (m)

H = height in metres (m)

Simplified 28 A machines lifts a load of weight 2500µ through a vertical distance of 3m in 1.5seconds what is the power of the machine.

Solution

Power = workdone

Time

But workdone = force x distance

= 2500 x 3 = 7500

Simplified 29 A cranes lift a load of weight 4,500µ through a distance of 15m in 10seconds. What is the power of the crane in

Watt

horse power

Solution

Power = force x distance

Time

= 4,500 x 15 = 6750w

(b) 1kw = 1000

6750watt = 6750 = 6.75kw

1000

1 horse power = 746watt

6750watt = 6750 = 9lip

746

WORK ENERGY RESOURCES

They word energy resources are classified into

Renewable Energy

Solar (b)wind (c) water (d) biomass

(2) Non-renewable

(a) Nuclear (b) petroleum and natural gas

EXERCISE

A bullet of mass 0.05kg has a speed of 400m51, what is its kinetic energy if it strikes a wall whose average resisting force is 10,000 calculate the distance penetrated

Ans 400J, 0.4m