KE, GPE & EPE (AQA GCSE Physics): Revision Note

The diagram below shows a student before and after a bungee jump. The bungee cord has an unstretched length of 30.0 m.

The mass of the student is 60.0 kg. The gravitational field strength is 9.8 N / kg.

Calculate:

a) The change in gravitational potential energy of the student at 30.0 m

b) The maximum change in the gravitational potential energy of the student

c) The speed of the student after falling 30.0 m if 90% of the energy in the student's gravitational potential store is transferred to the student's kinetic store

d) The spring constant of the bungee cord if all the energy in the gravitational potential store of the student is transferred to the elastic potential store of the bungee cord

Answer:

Part (a)

Step 1: List the known quantities

• Mass of the student, m = 60.0 kg

• Gravitational field strength, g = 9.8 N/kg

• Change in height, h = 30.0 m

Step 2: Write out the equation for gravitational potential energy

$E_P=mgh$

Step 3: Calculate the change in gravitational potential energy

$E_P=60\times 9.85\times 30$

$E_P=17640\mathrm{J}$ 

Part (b)

Step 1: List the known quantities

• Mass of the student, m = 60.0 kg

• Gravitational field strength, g = 9.8 N/kg

• Maximum change in height, h = 75.0 m

Step 2: Calculate the maximum change in gravitational potential energy

$E_{Pmax}=mg{h}_{max}$

$E_{Pmax}=60\times 9.8\times 75$

$E_{Pmax}=44100\mathrm{J}$ 

Part (c)

Step 1: List the known quantities

• Mass of the student, m = 60.0 kg

• $E_P$ at 30.0 m = 17 640 J

Step 2: Determine 90% of the $E_P$ at 30.0 m 

$E_K=90\%\mathrm{of}{E}_P$

$E_K=0.9\times 17640$

$E_K=15876\mathrm{J}$

Step 3: Write out the equation for KE

$E_K=\frac{1}{2}m{v}^2$

Step 4: Rearrange to make speed the subject

• Multiply both sides by 2:

 $m{v}^2=2\times E_K$

• Divide both sides by m:

 $v^2=\frac{2\times E_K}{m}$

• Take the square root of both sides:

 $v=\sqrt{\frac{2\times E_K}{m}}$

Step 5: Calculate the speed

 $v=\sqrt{\frac{2\times 15876}{60}}$

$v=23.0\mathrm{m}/\mathrm{s}$ 

Part (d)

Step 1: List the known quantities

• $E_{Pmax}$ = 44 100 J

• $E_e$ at 75.0 m =  $E_{emax}$ 

Step 2: Determine the extension of the bungee cord 

$e=75.0-30.0$

$e=45.0\mathrm{m}$

Step 3: Write out the equation for elastic potential energy

$E_e=\frac{1}{2}k{e}^2$ 

Step 4: Rearrange to make spring constant, k, the subject

• Multiply both sides by 2:

 $k{e}^2=2\times E_e$

• Divide both sides by $e^2$:

 $k=\frac{2\times E_e}{e^2}$

Step 5: Calculate the spring constant

 $k=\frac{2\times 44100}{{45}^2}$

$k=43.6\mathrm{N}/\mathrm{m}$

If a question asks you to "state" a value, you do not need to carry out a calculation: The answer will almost certainly be a number either from a previous answer or which was given somewhere in the question.

For example, if you have just calculated the gravitational potential energy of an object and are then asked to state the kinetic energy a moment later, the answers are very likely to be the same.