Work
Work is the measure of the amount of energy converted from one form
into another by a force which produces a displacement. Hence the unit
for work is the joule (J).
i.e. work = force x displacement in the direction of the force
W = F.d
Note that the product of two parallel vectors is a scalar.
If the force and displacement vectors are not in the same direction, then
the component of one in the direction of the other must be used.
W = F d cosθ
N.B. It does not matter whether you
use F cos θ times d or d cos θ times F.
Hooke's Law
Robert Hooke studied the properties of
elastic materials, particularly springs. He
discovered that the extension of a spring
is directly proportional to the applied
force. This is known as Hooke's Law.
(This is one of the few things that he
gets credit for that was not plagiarized
by Newton.
The constant, k, in the equation F = kx is called the spring constant or
the stiffness of the spring. Unit Nm-1.
Note that Newton gets credit even here.
In this case the force is not constant, but the average force is ½ F and
the displacement is x.
The work is represented by the area under the force-displacement
graph. The energy is stored as elastic potential energy.
So, W = ½ F x or W = ½ kx2
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Kinetic Energy
A body in motion has kinetic energy. Translational, rotational and
vibrational kinetic energy are all forms of kinetic energy.
Consider a steady force causing a body of mass m to accelerate from
rest to a velocity v, and therefore giving it translational kinetic energy.
v2 = u2 + 2as
v2 = 2as
v2 = 2Fs/m
but u = 0 so
but a = F/m so
but Fs = work done
Work done = EK = ½mv2
Gravitational Potential Energy
If two bodies exert an attractive force on each other, then work must
be done to separate them. This change in position relative to the other
produces a change in potential energy. If they are released, the
attractive force will convert this stored energy into kinetic energy as
they accelerate towards each other.
Consider a mass, m lifted a height Δh
from the earth's surface. The lifting
force necessary is equal to the
weight of the object.
Work = force . displacement
= mg . Δh
Gravitational Potential Energy E = mgΔh
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Conservation of Energy
The principal of Conservation of Energy states that:
"The total energy of the universe is constant" or
"Energy can be neither created nor destroyed; only changed from one
form into another."
If we are dealing with a system smaller than the whole universe, then
energy will be conserved as long as there is no net transfer of energy into
or out of the system. In that case, the gain of one type of energy must
balance the loss of another type of energy. An important consideration is
whether there is a friction force doing work converting energy into heat
energy. If you are told to "ignore air resistance" or that a surface is
"smooth", meaning frictionless, then this can be ignored in a problem.
Elastic and inelastic collisions
In a collision, momentum is conserved. Kinetic energy may be conserved, in
which case the collision is described as "elastic". Kinetic energy is not
conserved in an "inelastic" collision. In that case, work is done
compressing the colliding objects, or the ground, producing other forms of
energy. A collision may trigger a release of chemical or elastic energy.
Power
Power is defined as the rate of energy conversion or the rate at which
work is done.
Power = work done / time taken
P = ΔW/Δt
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Unit: watt (W = Js )
Efficiency
When energy is converted from one form to another, some of the energy
is usually converted to heat by the forces of friction. This is essentially a
non-useful form of energy. The efficiency of an energy conversion
process is a measure of the proportion of energy converted into the
desired useful form. It is usually expressed as a percentage.
Efficiency = Useful energy output x 100%
Energy input
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