Mechanics Tutorial 12 - Conservation of Energy

The Law of Conservation of Energy States:

Energy is neither created nor destroyed; it is converted from one form to another.


At GCSE you would have done some energy chains, for example in a nuclear power station.  


      The above nonsense (including spelling mistake) is reproduced from a student's answer in a test!  Please be a good chap and don't write drivel like this.



Potential Energy

This term is often used in the context of gravitational potential energy.  If we lift an object of mass m against gravity, we are doing a job of work.


Work done = PE = weight × distance moved against gravity.


DEp = mgDh


Question 1

Explain what each of the terms in the equation DEp = mg × Dh mean.                  


Question 2

What is the potential energy of a 12 kg mass raised to a height of 25 m?




Kinetic Energy

Kinetic energy is the ability to do work through motion.  If the motion is in a straight line, we call the kinetic energy translational


Kinetic energy is given by the equation:

kinetic energy (J) = 1/2 × mass (kg) × (speed (m/s))2

In Physics Code:

Suppose we use a force F to accelerate an object steadily from zero up to a speed v. The kinetic energy is the same as the work done.

Kinetic energy (J) = force (N) × distance moved (m) .......Eq 1


Force (N) = mass (kg) × acceleration (m/s2)

we can write:

Force (N) = mass (kg) × [change in speed (m/s) ÷ time (s)]

In Physics code:

F = m × [(v - 0) ÷ t] = m × v/t


distance travelled = average speed × time

In Physics code:

d = [(v - 0) ÷ 2] × t = 1/2 v × t .........Eq 2

Combining equations 1 and 2:

Kinetic energy = F × d

Ek = m × v/t × 1/2 v × t

The t terms cancel out to give us:

Ek = 1/2 mv2

The ability to follow this derivation is the sort of thing that will distinguish the outstanding student (A*) from the excellent student (A).



Question 3

Calculate the kinetic energy of a 4 kg shot-put thrown by an athlete at a speed of 15 m/s.



Note that we have talked about speed rather than velocity. The kinetic energy of an object is the same regardless of direction. We can say this, because of we have a negative velocity, the kinetic energy will still be positive, since minus times a minus is a plus.



Potential Energy converted to Kinetic Energy

If an object falls, the potential energy is turned into kinetic energy.  Then we combine the equations for Ep and Ek (conservation of energy):


Ep = Ek,

mgDh = ½ mv2

mgDh = ½ mv2 [masses cancel]

Ž v2 = 2gDh


Question 4

A coin is dropped from the viewing platform of an observation tower 80 m high.   How fast will it travel just before it hits the ground? Answer

Question 5

Explain why you do not need the mass of the coin in the question above.
Renewable Energy
Many chemical energy resources such as fossil fuels have the advantage that their energy is in very concentrated form.  50 litres of diesel fuel can take a car 1000 km.  They have the two main disadvantages:



Electric cars do not have these problems.  However their range is limited by their batteries to about 100 – 200 km at best.  Electric cars are nothing new; they were around long before petrol cars.  However the limitations of the batteries have always been a problem.


Most renewable energy projects centre on the generation of electricity.  Each has its advantages and disadvantages, as shown in the table below:


Renewable Source




Uses running water of which there is plenty.


Can be turned on and off quickly

Usually needs a dam to block off a valley to make a reservoir.



Relatively inexpensive

No emissions.

Can be set up in any windy spot.

Useless on a calm day

Cannot work if the wind is too strong

Often not welcomed by local people.

Can disturb birds on migration.

Solar Cells

The intensity of the Sun is 500 W m-2

Huge amounts of energy can be harvested.

Solar cells are expensive.

Use scarce resources


Need large panels

Not that effective on dull days.

Solar heating

Suns rays can be concentrated with mirrors.

Lots of heat in a small space.

Needs large mirrors.

Mirrors need to track the sun.

Does not work well on a cloudy day.

Potentially dangerous with intensely concentrated rays of light

Solar panels

Can be placed on any roof of a house.

Make lots of hot water.

Water needs to be stored.

Ineffective on a cloudy day.



New plants can be grown to replace the fuel

Valuable agricultural land taken up for biomass crops.

Low energy concentration of biomass fuels.


Uses waste material such as rubbish and sewage.  Unlimited supply of these materials.

People don’t like using it as they are put off by the thought of the source.


Large amounts of power from tidal flows

Will be there as long as the Moon’s there (and nobody is going to take it away).

Environmental considerations, e.g. loss of habitat for wading birds.

Power produced according to tides, not when people want it.

Very expensive.


A lot of energy available in waves.

Useful for countries with long coastlines.

Machines need to be set up in hostile environments.

Often damaged by storms.


Unlimited heat from the centre of the Earth

On most places, deep drilling has to take place to get rocks of adequate temperature.  Steam can leak through cracks in the rocks.

Best in volcanic areas.