Physics 101 Learning Object: Energy in SHM Multiple choice question

Q1.) A bungee jumper with a mass of 75kg jumps off of a 42m bridge above a river. Assume that the bungee with a spring constant (K) of 650N/m stretches to a maximum of 40m with the jumper attached. At what distance (x) from the top of the bridge will the potential energy of the jumper (U) be equal to the kinetic energy of the jumper (K)?

A) 10.1m B) 8.3mC) 14.1mD) 16.3m

Picture from: http://artsonearth.org/wp-content/uploads/2013/02/bungy-jumping-off-the-kawarau-bridge-photo_1417194-fit468x296.jpg

Question: A bungee jumper with a mass of 75kg jumps off of a 42m bridge above a river. Assume that the bungee with a spring constant (K) of 650N/m stretches to a maximum of 40m with the jumper attached. At what distance (x) from the top of the bridge will the potential energy of the jumper (U) be equal to the kinetic energy of the jumper (K)?

Answer: C, 14.1m

Explanation: Since the total energy of a system in simple harmonic motion is equal to the sum of the potential energy and the kinetic energy, they must be equal when each component is equal to half of the energy of the system. To determine this you determine the total energy of the system and divide it by half, then equate this to the equation for the potential energy of the system and solve for x (the distance from the top of the bridge). See calculation below.