A trampoline is made from a sheet of material held in place by stretched springs - AQA - GCSE Physics Combined Science - Question 3 - 2022 - Paper 1

The elastic potential energy of the springs increases as the spring is compressed when the child lands. At position A, the springs are in their relaxed state. Upon the child's landing at position B, the springs store energy in the form of elastic potential energy.

The surroundings experience an increase in thermal energy due to the energy dissipation from the trampoline's material and the air around it when the child lands. This energy transfer results in a slight increase in the internal energy of the surrounding particles.

To determine the extension of each spring at position B, we use the formula for elastic potential energy:

$e = \frac{1}{2} k x^2$

Given:

• At position A, the potential energy per spring is 4.9 J;
• The spring constant, ( k ), is calculated using the stretch at position A:

$k = \frac{4.9}{0.5 \times 0.056^2} = 3125 \text{ N/m}$

• At position B, the energy is increased to 8.1 J:

$8.1 = \frac{1}{2} \times 3125 \times e^2$
Solve for ( e ):

e = \sqrt{\frac{2 \times 8.1}{3125}} = 0.072 \text{ m}$$

The work done by the child is equal to the total energy transferred by the child. This is because, during the bouncing motion, the energy is utilized in moving against forces, and it ultimately relates to the energy transferred to the trampoline.