Gravitational Potential Energy (AQA GCSE Combined Science: Synergy: Physical Sciences): Revision Note

A man of mass 70 kg climbs a flight of stairs that is 3 m higher than the floor. Gravitational field strength is approximately 9.8 N/kg.

Calculate the energy transferred to the man's gravitational potential energy store.

Answer:

Step 1: List the known quantities

• Mass of the man, m = 70 kg

• Gravitational field strength, g = 9.8 N/kg

• Height, h = 3 m

Step 2: Write down the equation for gravitational potential energy

• This equation is given on the Physics Equations Sheet

$E_p=m\times g\times h$

Step 3: Substitute the known values and calculate the gravitational potential energy

• All three values are already in the units the equation needs, so they can go straight in

$E_p=70\times 9.8\times 3$

$E_p=2058\text{ J}$

A person on a zip wire loses 1.47 kJ of gravitational potential energy. The person has a mass of 60 kg and g = 9.8 N/kg.

Calculate the change in vertical height.

Answer:

Step 1: List the known quantities

• Change in gravitational potential energy, E_p = 1.47 kJ

• Mass of the person, m = 60 kg

• Gravitational field strength, g = 9.8 N/kg

Step 2: Convert the energy into joules

• The equation needs energy in joules, and 1 kJ = 1000 J

$E_p=1.47\times 1000=1470\text{ J}$

Step 3: Write down the equation for gravitational potential energy

$E_p=m\times g\times h$

Step 4: Rearrange the equation to make height the subject

• Divide both sides by m × g:

$h=\frac{E_p}{m\times g}$

Step 5: Substitute the known values and calculate the height

$h=\frac{1470}{60\times 9.8}$

$h=\frac{1470}{588}$

$h=2.5\text{ m}$

In AQA GCSE Physics exams, the value of g is always given in the question (usually 9.8 N/kg), so use the value you are given. You do not need to memorise it. Questions often give the energy and ask for the height or the mass. Rearrange the equation first. Convert kJ to J before you substitute