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There are two requirements for work to be done
1. There must be a force acting on the object
2. The object must move parallel to the force that is in the same or opposite direction as
the force.
Note: if the force and the distance are perpendicular (at right angle), no work is done.
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PRINCIPLE OF CONSERVATION OF ENERGY
The principle of conservation of energy states that,” Energy can neither
be created nor destroyed but it can be transformed from one form to
another”
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ENERGY TRANSFORMATION IN A SWINGING PENDULUM
Diagram C illustrates a situation in which Gravitational Potential Energy is
converted into Kinetic energy. This situation involves a pendulum swinging back
and forth. Initially, the pendulum mass is raised to a height of say .5m above it's
original resting position at point "C". At this point the pendulum has it's greatest
GPE. The GPE can be calculated using GPE=mgh. When lifted to point "A" the
pendulum mass gains 4.9J of GPE ( Note: This also means that 4.9J of work has to
be done to lift the pendulum mass to this starting point. See PS 6.3 ) When the
pendulum is released and falls towards point "C" the mass gains velocity, and
therefore Kinetic Energy on the way down. By the time the pendulum reaches
point "C" it has its maximum velocity and 100% of the GPE has been converted to
Kinetic energy. This process reverses as the pendulum continues its swing from
point "C up to point "E". By the time the pendulum mass reaches point "E" the
Kinetic Energy it had at point "C" has been entirely converted to GPE
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Power
Power is the rate of work done in a unit of time.
It can be misunderstood by most of the students. They think more power the
machine has it does more work. However, power just shows us the time that the
work requires. For example, same work is done by two different people within
different times, say one does the work in 5 minutes and the other in 8 minutes,
thus the man who did the work n 5 minutes is more powerful. the shorter the
time the more the power. let us see it mathematically.
The unit of power from the definition above is joules/second, generally we use
the unit of power as watt.
1 joule/second = 1 watt
Work done by a Torque
What is torque?
Torque is a measure of the force that can cause an object to rotate about an axis. Just as force
is what causes an object to accelerate in linear kinematics, torque is what causes an object to
acquire angular acceleration.
Torque is a vector quantity. The direction of the torque vector depends on the direction of the
force on the axis.
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Generally
Torque = Force X radius X sine Ø
When the angle between is 90 degrees then
Sine 90 = 1
Torque = Force applied in N X radius in m.
The SI unit for torque is the Newton-meter.
Work done
Workdone is the force multiplied with distance moved by the force.
It can be expresses as
W = Fs
Where
W= workdone(J, Nm)
F= force (N)
S= distance moved by force(m)
For an angular motion
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Workdone can be expressed as
W = FQr
= TQ
Where
W= work(joules)
Q= angle(radian)
r= radius(m)
T=torque (Nm)
POWER TRANSMITTED by Torque
Power is the ratio between the workdone and the time taken.
Powe is expreesed as
workdone
Power =
time
TQ
=
t
Q
But =w
t
Then
Power = T X w
Power = torque X angular velocity
Example
1. The engine of a vehicle develops 40 kW at a speed of 900 rev/min. Calculate the torque
required.
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More questions
1. An object has a mass of 5 kg. What is its kinetic energy if its speed is
I. 5 m/s
II. 10 m/s
2. What is the kinetic energy of a 12g bullet travelling at 320 m/s?
3. A Stone of 2 kg falls from a height of 25m above the ground. Calculate the P.E possessed by the
stone.
4. How much power is required to accelerate a 1000 Kg car from rest to 26.7 m/s in 8 s?
5. A stone of mass 500 g is thrown vertically upwards with a velocity of 15 m/s. Find
I. The potential energy at greatest height
II. The kinetic energy on reaching the ground
(Assume g = 10m/s2)
