Question

Pierce is bungee jumping off of the top of a 75 meter tall dam in Russia with a cord that is too long. When he splashes into the water at the bottom of the dam he is moving at a speed of 8.0 m/s, and the bungee cord is stretched to be 25 m longer than its rest length. If the bungee cord has a spring constant of 160 N/m, what is Pierce's mass in kilograms? (Ignore air resistance) 

Answer 1

Using energy conservation:

KEi + PEi = KEf + PEf

KEi = Initial kinetic energy of bungee jumper = 0, Since initial speed is zero

PEi = Initial potential energy at the top of Dam = m*g*H + 0 (Spring PE will be zero since no stertching at the top)

H = height of dam from reference point (water level) = 75 m

KEf = (1/2)*m*V^2, where V = final speed of block at the surface of water = 8.0 m/s

PEf = final potential energy = 0 + (1/2)*k*x^2 (Gravitational PE will be zero at reference point)

So,

0 + m*g*H + 0 = (1/2)*m*V^2 + (1/2)*k*x^2

k = spring constant = 160 N/m

Using given values:

m*(g*H - V^2/2) = (1/2)*k*x^2

m = k*x^2/(2*g*H - V^2)

m = 160*25^2/(2*9.81*75 - 8.0^2)

m = 71 kg = mass of Pierce

Correct option is E.

Answer 2

Answer 3