Kinetic energy
All moving objects have kinetic energy, \(E_{k}\).
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
Question
What is the kinetic energy of a 1000 kg car travelling at 5 m/s?
\(E_{k}\) = \(\frac{1}{2}\) mv2
m = 1000 kg
v = 5 m/s
\(E_{k}\) = \(\frac{1}{2}\) 1000 kg x (5 m/s)2
\(E_{k}\) = 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 kg x v2
175,000 = 600 kg x v2
v2 = \(\frac{175,000 J}{600 kg}\)
v2 = 291.67
v = \(\sqrt{291.67}\)
v = 17.1 m/s
The car has a speed of 17.1 m/s.