Solve Energy Stored Problem: 70kg Man, 85m Fall, 50m Bungee

[Rampage]

Im really stuck with this question, hoping someone could give me a hand

A bungee rope of unstretched length 50M is designed to allow a 70Kg man to come to rest 85m below the platform from which he jumps.

Calculate the energy stored in the rope when the man has come to rest. Ignore the weight of the rope.
(Gravitational field strength 9.8)


Calculate the gravitational potential energy lost by the man when he comes to rest.


Am i right to do
70 x 9.8 = 686N
Work Done = Force x Displacement
=24.1Kj?

Im not sure if I am using the correct formula, and I am totally stuck on the 2nd part

 

[pervect]

Am i right to do
70 x 9.8 = 686N

Yes, that's right so far

Work Done = Force x Displacement
=24.1Kj?

The displacement is wrong

Im not sure if I am using the correct formula, and I am totally stuck on the 2nd part

The second part is the key to the problem.

Try reading

http://id.mind.net/~zona/mstm/physics/mechanics/energy/gravitationalPotentialEnergy/gravitationalPotentialEnergy.html

 

[GSXR750]

To solve this problem, we first need to calculate the total distance the man falls, which is 85m + 50m = 135m. Then, we can use the formula for potential energy, PE = mgh, where m is the mass (70kg), g is the gravitational field strength (9.8m/s^2), and h is the height (135m). Plugging in these values, we get PE = (70)(9.8)(135) = 92,430 J. This is the total gravitational potential energy lost by the man when he comes to rest.

As for the energy stored in the rope, we can use the formula for elastic potential energy, PE = 1/2kx^2, where k is the spring constant and x is the displacement. In this case, the displacement is the difference between the unstretched length (50m) and the stretched length (85m), which is 35m. The spring constant can be calculated by dividing the weight of the man (686N) by the displacement (35m), which gives us a value of 19.6 N/m. Plugging these values into the formula, we get PE = 1/2(19.6)(35)^2 = 12,740 J. This is the energy stored in the rope when the man has come to rest.

In summary, the man loses 92,430 J of gravitational potential energy, and the rope stores 12,740 J of elastic potential energy. I hope this helps you understand the problem better and solve it successfully.