Calculating KE & Changes in GPE

Higher Tier

Kinetic Energy

Kinetic energy can be calculated using the equation:

$k i n e t i c e n e r g y = \frac{m a s s \times v e l o c i t y^{2}}{2}$

$K E = \frac{1}{2} m v^{2}$

Where:
- KE = kinetic energy in joules (J)
- m = mass of the object in kilograms (kg)
- v = speed of the object in metres per second (m/s)

Kinetic Energy of a Moving Car

Kinetic Energy Car, downloadable AS & A Level Physics revision notes

A moving car has kinetic energy because of its mass and speed

Worked example

Calculate the kinetic energy of a vehicle of mass 1200 kg moving at a speed of 27 m/s.

Answer:

Step 1: List the known quantities

Mass of the vehicle, m = 1200 kg
Speed of the vehicle, v = 27 m/s

Step 2: Write down the equation for kinetic energy

$K E = \frac{1}{2} m v^{2}$

Step 3: Calculate the kinetic energy

$K E = \frac{1}{2} \times 1200 \times 27^{2}$

KE= 437 400 J

Step 4: Round the final answer to 2 significant figures

KE = 440 000 J

Examiner Tip

When performing calculations using the kinetic energy equation, always double-check that you have squared the speed. Forgetting to do this is the most common mistake that students make.

Change in Gravitational Potential Energy

The change in gravitational potential energy, PE, of an object can be calculated using the equation:

change in gravitational potential energy = mass × gravitational field strength × height

PE= mgh

Where:
- PE = change in gravitational potential energy, in joules (J)
- m = mass, in kilograms (kg)
- g = gravitational field strength in newtons per kilogram (N / kg)
- h = change in height metres (m)

Gravitational Potential Energy of a Mass

gpe man, IGCSE & GCSE Physics revision notes

Raising a mass to a height above the ground gives it gravitational potential energy

Worked example

A man of mass 70 kg climbs a flight of stairs that is 3 m higher than the floor.

Gravitational field strength, g = 10 N/kg.

Calculate the change in the man's gravitational potential energy.

Answer:

Step 1: List the known quantities

Mass of the man, m = 70 kg
Gravitational field strength, g = 10 N/kg
Change in height, Δh = 3 m

Step 2: Write down the equation for gravitational potential energy

PE = mgh

Step 3: Calculate the gravitational potential energy

PE = 70 × 10 × 3

PE = 2100 J

Calculating KE & Changes in GPE (WJEC GCSE Physics: Combined Science)

Revision Note