Download Kinetic and Potential Energy

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What is energy?
Energy is the measure of the ability of an object or a
system to perform work. There are many types of energy:

kinetic energy – energy of an object due to its speed

gravitational potential energy – energy of an object due
to position in a gravitational field

elastic energy – energy stored when an object is
stretched or compressed

chemical energy – energy stored in chemical bonds

nuclear energy – energy stored in nuclei.
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Energy transfer
When work is done, energy is
transferred. That energy might be:

gravitational potential energy
– e.g. when an object
changes height within a
gravitational field

kinetic energy – e.g. when
an object changes speed

light energy – e.g. when a
light bulb is switched on

heat and sound – e.g. when
a car brakes sharply.
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Conservation of energy
The law of conservation of energy states that:
Energy cannot be created or destroyed;
it can only be changed into another form.
In other words, the total energy
of a system is constant.
A bungee jumper’s
gravitational potential energy
is changed into kinetic energy
as they jump, and then stored
as elastic potential energy as
the bungee rope stretches.
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What is gravitational potential energy?
Gravitational potential energy (GPE, Ep or Egrav) is the
energy of an object due to its position in a gravitational field.
The Ep gained by a mass is proportional to the force used to
lift it, and the distance it is lifted:
gravitational
= mass × gravitational × height
potential energy
field strength
Ep = mgh
It is often talked about in terms
of a change in an object’s Ep
due to a change in its height:
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ΔEp = mgΔh
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Ep: example question 1
A supermarket employee lifts a can
of baked beans, weighing 250 g,
from the floor, to a shelf 2 m high.
How much gravitational potential
energy does it gain?
(g = 9.81 N kg-1)
ΔEp = mgΔh
= 0.250 × 9.81 × 2
= 4.9 J
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Ep: example question 2
A pole vaulter of mass 80 kg
jumps a height of 5 m. What is
his gravitational potential
energy at the highest point of
his jump?
(g = 9.81 N kg-1)
Ep = mgh
= 80 × 9.81 × 5
= 3924 J
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Work done using slopes
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What is kinetic energy?
Kinetic energy (KE or Ek) is the energy of an object due to
its speed.
kinetic energy = ½ × mass × speed2
Ek = ½mv2
Where:

kinetic energy is measured in joules (J)

mass is measured in kilograms (kg)

speed is measured in meters per second (ms-1).
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Deriving Ek = ½mv2
Consider a force F acting on an object of mass m, initially at
rest, moving it a distance s in time t.

From ‘suvat’ equations:
s = ½ (u + v)t
a = (v – u) / t

Because u = 0 ms-1:
s = ½vt
a=v/t

Newton’s 2nd law:
F = ma

Substituting a = v / t:
F = mv / t

Work done by force:
W = Fs
W = (mv / t) × ½vt
W = ½mv2

Work done = energy transferred:
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Ek = ½mv2
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Ek and Ep
If resistive forces, such as friction and air resistance, are
ignored, Ek and Ep are related as follows:
loss of Ek = gain in Ep
lose of Ep = gain in Ek
For example, if an object of mass m is released above the
ground at height h, it will gain speed, v, as it falls.
Due to the conservation of energy, and assuming air
resistance is negligible, after falling a height of Δh:
½mv2 = mgΔh
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Conservation of energy: example question
A ball of mass 400 g is thrown upwards at a speed of 5 ms-1.
(g = 9.81 N kg-1).

What is the ball’s Ek as it is released?
Ek = ½mv2
= ½ × 0.4 × 52
= 5J

What is the ball’s maximum gain of Ep?
ΔEp = Ek
= 5J

What is the ball’s maximum height?
Ep = mgh
h = Ep / mg
= 5 / (0.4 × 9.81)
= 1.27 m
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Resistive forces
Resistive forces are forces that act on a moving body in the
opposite direction to the direction of movement.
The main resistive force is friction, which includes drag or
air resistance.
When an object such as a rollercoaster moves vertically
without a driving force, any difference between a change in
ΔEp and ΔEk corresponds to a loss of energy to resistive
forces, or work done against resistive forces:
W = ΔEp + ΔEk
Where ΔEk is positive if ΔEp
is negative, and vice versa.
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Investigating Ek and Ep
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Energy calculations
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