Kinetic energy

The store of energy of a moving object is called its kinetic energy.

The amount of kinetic energy of a moving object can be calculated using the equation:

kinetic energy = \frac{1}{2} × mass × speed2

E_{k} = \frac{1}{2} m~v^2

This is when:

  • kinetic energy (Ek) is measured in joules (J)
  • mass (m) is measured in kilograms (kg)
  • speed (v) is measured in metres per second (m/s)

Example

An apple of mass 100 g falls from a tree. It reaches a speed of 6 m/s before landing on Isaac's head. What is the gain of kinetic energy of the apple?

E_{k} = \frac{1}{2} m~v^2

E_{k} = \frac{1}{2} \times 0.1 \times 6^2

E_{k} = \frac{1}{2} \times 0.1 \times 36

E_{k} = 1.8~J

Question

How much kinetic energy does a 30 kg dog have when it runs at 4 m/s?

E_{k} = \frac{1}{2} m~v^2

E_{k} = \frac{1}{2} \times 30 \times 4^2

E_{k} = \frac{1}{2} \times 30 \times 16

E_{k} = 240~J

Gravitational potential energy

If an object is raised, its store of gravitational potential energy increases. As it falls, its gravitational potential energy decreases.

The amount of gravitational potential energy stored by an object at height can be calculated using the equation:

gravitational potential energy = mass × gravitational field strength × height

E_{p} = m~g~h

This is when:

  • gravitational potential energy (Ep) is measured in joules (J)
  • mass (m) is measured in kilograms (kg)
  • gravitational field strength (g) is measured in newtons per kilogram (N/kg)
  • height (h) is measured in metres (m)

Example

Galileo takes a 5 kg cannonball to the top of the Tower of Pisa for one of his experiments. The tower is 56 m high. How much gravitational potential energy has the cannonball gained? (g = 10 N/kg)

E_{p} = m~g~h

 E_{p} =  5 \times  10 \times 56

 E_{p} = 2,800~J

Question

How much gravitational potential energy does a 500 g book gain when it is lifted up 1.5 m onto a shelf?

E_{p} = m~g~h

E_{p} = 0.5 \times 10 \times 1.5

E_{p} = 7.5~J

For any of these equations you may need to change the subject of the formula.