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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

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.

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)

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.

Workdone = force x distance
W = mg x h
M =?, w = 450, h = 300cm = 3m
450 = mx10x3
450 = 30m
M = 450 = 15kg

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


Solar energy
Nuclear energy
Chemical energy
Heat energy
Sound energy
Light energy
Mechanical energy
Electrical energy etc

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
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.

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

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)

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.
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

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.

Power = workdone
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
horse power

Power = force x distance
= 4,500 x 15 = 6750w
(b) 1kw = 1000
6750watt = 6750 = 6.75kw
1 horse power = 746watt
6750watt = 6750 = 9lip
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

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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