Higher Tier: Kinetic Energy
Kinetic energy is the energy of a moving object.
Any object that is moving has kinetic energy.
The amount of kinetic energy of an object has depends on its:.
- mass;
- speed of the object.
Calculating kinetic energy
The kinetic energy of a moving object can be calculated using the equation:
Kinetic energy = \(\frac{1}{2}\) x mass x (speed)2
Kinetic energy = \(\frac{1}{2}\) mv2
or
\(E_{k}\) = \(\frac{1}{2}\) mv2
where:
\(E_{k}\) = kinetic energy in joules, J
m = mass in kg
v = speed in m/s
Example
What is the kinetic energy of a 1000 kg car travelling at 5 m/s?
Answer
\(E_{k}\) = \(\frac{1}{2}\) mv2
m = 1000 kg
v = 5 m/s
\(E_{k}\) = \(\frac{1}{2}\) x 1000 x (5)2 (Note that it is only the speed that鈥檚 squared).
\(E_{k}\) = 12,500 J
The car has 12,500 J of kinetic energy
Question
A car of mass 1200 kg, travelling at a steady speed, has a kinetic energy of 175 kJ. What is the speed of the car?
\(E_{k}\) = \(\frac{1}{2}\) mv2
The car has 175 kJ of kinetic energy. This must be converted into J to use in the equation for kinetic energy.
175 kJ = 175,000 J
\(E_{k}\) = 175,000 J
m = 1200 kg
175,000 = \(\frac{1}{2}\) x 1200 x v2
175,000 = 600 x v2
v2 = \(\frac{175,000}{600}\)
v2 = 291.67
v = \(\sqrt{291.67}\)
v = 17.1 m/s
The car has a speed of 17.1 m/s.
Conservation of energy and kinetic energy
The car in the above question has 175,000 J of kinetic energy when travelling at a speed of 17.1 m/s.
When it stops it has zero kinetic energy.
So, where has the kinetic energy gone?
From the principle of conservation of energy, energy can never be destroyed; it can only be transferred from one form to another.
If the car is stopped using the brakes, the kinetic energy is mainly converted to heat energy in the brakes, and they become hot.
This heat energy then spreads out to the surroundings.
There is some sound energy which also spreads out.
As the car brakes: kinetic energy \(\rightarrow\) heat energy.