K323 / 2027
Energy overview

Topic 2 of 6

Kinetic and gravitational energy

Kinetic energy depends on mass and speed. A change in gravitational potential energy near Earth depends on mass and vertical height change.

Use mass in kg, speed in m/s and height in m. Gravitational field strength g is measured in N/kg. Review unit conversions before substituting.

Kinetic energy: Ek = 1/2 mv2m = mass in kg; v = speed in m/s. Ek is measured in J. Square the speed, not the whole expression.

Worked example

A moving 2.0 kg object

At a speed of 4.0 m/s:

Ek = 0.5 x 2.0 x 4.02 = 0.5 x 2.0 x 16 = 16 J.

At 8.0 m/s, the same mass has Ek = 0.5 x 2.0 x 64 = 64 J. Doubling the speed makes the kinetic energy four times as large.

  • At fixed speed, doubling the mass doubles kinetic energy.
  • At fixed mass, doubling speed multiplies kinetic energy by four; halving speed makes it one quarter.
  • The direction of motion does not change this calculation. Use speed, and give energy in J without a spatial direction.

Use a vertical height change

Gravitational potential energy change = mghm = mass in kg; g = gravitational field strength in N/kg; h = vertical height change in m. The result is in J. Near Earth, take g as approximately constant over the height considered.

Raising a mass increases the gravitational store of the mass-Earth system; lowering it decreases the store. The numerical value Ep = mgh is measured relative to a chosen zero-height level. Changing that reference changes the assigned value, but not the energy change between the same two positions.

Worked example

Raise a load through 1.5 m

A total mass of 2.0 kg is raised vertically by 1.5 m. Use g = 10 N/kg.

Increase in Ep = 2.0 x 10 x 1.5 = 30 J.

Its weight is mg = 20 N. Lifting it to the same height along a longer ramp still increases the gravitational store by 30 J. Extra transfers due to friction would change the input required, not this gravitational change.

At fixed m and g, doubling the vertical rise doubles the gravitational store increase. At fixed rise and g, doubling the mass also doubles the increase. If the same load descends by 1.5 m, the store decreases by 30 J.

Rearrange for the quantity asked for

If the height change is unknown, h = change in Ep / (mg). For the 2.0 kg load, a 30 J increase at g = 10 N/kg gives h = 30 / (2.0 x 10) = 1.5 m.

If speed is unknown, first rearrange to v2 = 2Ek / m, then take the square root. Do not treat the value of v2 as the speed.

Height is not route length. Identify the starting and final vertical levels before using mgh. For kinetic energy, identify the speed at the instant being considered and square it.

Optional check A 0.50 kg load is taken up a ramp of length 2.0 m. Its final position is 0.80 m vertically above its starting position. Use g = 10 N/kg. What is its increase in gravitational potential energy?
A 0.50 kg load is taken up a ramp of length 2.0 m. Its final position is 0.80 m vertically above its starting position. Use g = 10 N/kg. What is its increase in gravitational potential energy?