Write down the equation which links gravitational field strength, gravitational potential energy, height and mass - AQA - GCSE Physics - Question 11 - 2018 - Paper 1

To calculate the change in gravitational potential energy when the student jumps, we use the formula:

$Ep = m imes g imes h$

Here, let’s assume the mass of the student is 50 kg (chosen for calculation purposes), g = 9.8 N/kg and h = 20.0 m.

Thus, the change in gravitational potential energy is:

$Ep = 50 imes 9.8 imes 20 = 9800 ext{ J}$

The change in kinetic energy that has been transferred is 80% of the change in gravitational potential energy:

$Kinetic ext{ Energy} = 0.8 imes 9800 = 7840 ext{ J}$

To find the speed (v) of the student after falling 20.0 m, we use the relationship between kinetic energy and speed:

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

Rearranging gives:

$v = \sqrt{\frac{2K.E}{m}}$

Substituting for K.E = 7840 J and m = 50 kg:

$v = \sqrt{\frac{2 \times 7840}{50}} = \sqrt{313.6} \approx 17.7 ext{ m/s}$

Therefore, to two significant figures, speed is:

$v \approx 18 ext{ m/s}$

The energy stored in the bungee cord at the lowest point is 24.5 kJ, which is:

$E = 24500 ext{ J}$

Using the formula for elastic potential energy:

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

where k is the spring constant and x is the extension. Given the extension is 35 m:

Rearranging gives:

$k = \frac{2E}{x^2} = \frac{2 \times 24500}{35^2} = \frac{49000}{1225} = 40 ext{ N/m}$