AQA · GCSE · Physics · Higher

Bungee Pod Maximum Height

Q06.2 6 marks

In a ride at a theme park, a person is strapped into a pod that is attached to two stretched bungee cords. The bungee cords behave like springs.

When the pod is released, the pod accelerates upwards.

Before the pod is released the extension of each of the two bungee cords is 8.0 m.

The spring constant of each bungee cord is 735 N/m.

The mass of the pod is 240 kg.

gravitational field strength = 9.8 N/kg

elastic potential energy = 0.5 × spring constant × (extension)²,

E_e=\tfrac12ke^2

gravitational potential energy = mass × gravitational field strength × height,

E_p=mgh

Calculate the maximum height reached by the pod.

Use the Physics Equations Sheet.

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Marking points

1 Uses Ee = 0.5ke² for one 8.0 m cord.
2 Finds 23 520 J for one cord and doubles it to 47 040 J for two cords.
3 Equates total elastic potential energy to mgh.
4 Rearranges for height and obtains 20 m, subject to official error-carried-forward guidance.

Full-mark answer

For one cord, $E_e=\tfrac12ke^2=0.5\times735\times8.0^2=23\,520\text{ J}$ . Two cords store $47\,040\text{ J}$ . At maximum height, $mgh=47\,040$ , so $h=47\,040/(240×9.8)=20text{ m}$.

Why this answer loses marks

I used only part of the total elastic energy before equating it to mgh.

Every stretched cord contributes to the launch, so combine all stored elastic energy before transferring it to gravitational potential energy.

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