# 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

30

**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 = 1/2MV

^{2}
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 mv

^{2}
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 mv

^{2}
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 = 10m5

^{2})
Solution

M = 50kg

H = 10m

V = ?

From equation of motion v

^{2}= u2 x 2gh
V

^{2}= 0x2x10x10
V

^{2}= 200
K.E = ½ MV

^{2}
= 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 = 1/2MV

^{2}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 = 2m5

^{2}
But a = 2m52 in equation (1)

v = 0 x 2 x 5 = 10m51

^{2}

**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 J5

^{1}
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

kw

horse power

Solution

Power = force x distance

Time

= 4,500 x 15 = 6750w

10

(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

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