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

Assuming the mass of the student is 50 kg, the change in gravitational potential energy can be calculated as:

$E_p = mgh = 50 ext{ kg} imes 9.8 ext{ N/kg} imes 20.0 ext{ m} = 9800 ext{ J}$

Thus, the change in gravitational potential energy is 9800 J.

80% of the change in gravitational potential energy has been transferred to the kinetic energy store. Therefore:

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

Using the kinetic energy formula:

$KE = \frac{1}{2} mv^2$

We can rearrange to find the speed (v):

$v = \sqrt{\frac{2 \cdot KE}{m}} = \sqrt{\frac{2 \cdot 7840 ext{ J}}{50 ext{ kg}}} \approx 17.7 ext{ m/s}$

Therefore, the speed of the student after falling 20.0 m is approximately 18 m/s when rounded to two significant figures.

The energy stored by the bungee cord is given as 24.5 kJ, which is equivalent to 24500 J. Using the formula for elastic potential energy:

$E = \frac{1}{2}kx^2$

Where k is the spring constant and x is the extension (35 m):

Rearranging gives:

$k = \frac{2E}{x^2} = \frac{2 \cdot 24500 ext{ J}}{35^2} = 40 ext{ N/m}$

Thus, the spring constant of the bungee cord is 40 N/m.