Bungee Jumper's Descent: Calculating Work Done by the Bungee Cord
How much work is done by the bungee cord on the jumper during his descent?
A bungee jumper makes a stunt jump in a jumping platform 10.87 m from above a height. The jumper weighs 413 N. If the jumper falls to within 42.73 m of the bottom of the height, how much work is done by the bungee cord on the jumper during his descent? Ignoring air resistance.
Final answer: The work done by the bungee cord on the jumper during his descent is -13160.18 Joules.
Calculation of Work Done by the Bungee Cord
The work done by the bungee cord on the jumper during the descent is governed by the change in gravitational potential energy. This is calculated by the formula PE = mgh, where m is the mass of the object, g is the acceleration due to gravity, and h is the height.
To calculate the work done, we first need to determine the change in height of the jumper. The total descent height is 10.87 m - 42.73 m = -31.86 m (negative because the jumper is moving downward).
The force exerted by the jumper due to gravity (weight) is 413 N. The work done by the cord is then calculated by multiplying the force and displacement in the direction of the force. Therefore, Work = Force x Displacement = 413 N x -31.86 m = -13160.18 J.
The negative sign in the result indicates that the work is done against the motion of the jumper, as the jumper is moving downward.