Calculating Closest Bungee Jump Distance

[snoitcelfer]

Homework Statement

an 80Kg bungee jumper steps off the jump platform which is 50m above the ground.
the bungee cord is 25m long when relaxed and has an E value of 8 MPa and a cross sectional area of 400mm^2.
Calculate the closest the jumper gets to the ground. Consider the center of gravity of the jumper to be at the end of the bungee cord.

Homework Equations

Energy conservation / strain energy

The Attempt at a Solution

i am stuck here because facing this problem i can find solutions using energy conservation such as mgh = (1/2)k(h-L)^2. however I have no idea how to get k from this as k = fx and i am not given a length with the jumper attached. so is it possible to find k from this information or do i need to go in a different direction?

 

[nvn]

snoitcelfer: Perhaps they want you to use the relaxed (initial) length L and assume k = E*A/L. But maybe someone will give a second opinion.

 

[Mene]

I would suggest using the strain energy equation to solve for the closest distance the bungee jumper gets to the ground. The strain energy equation is given by U = (1/2)kx^2, where U is the strain energy, k is the spring constant, and x is the displacement of the bungee cord. In this case, the displacement would be (25m - x), where x is the closest distance the jumper gets to the ground.

To find the spring constant, we can use the given information of the bungee cord's E value and cross sectional area. The formula for the spring constant for a bungee cord is k = (EA)/L, where E is the modulus of elasticity, A is the cross sectional area, and L is the relaxed length of the bungee cord. Plugging in the values, we get k = (8 MPa * 400mm^2) / 25m = 128000 N/m.

Now, we can plug this value of k into the strain energy equation and set it equal to the potential energy of the jumper at the highest point (mgh). This will give us the closest distance the jumper gets to the ground. The final equation would be (1/2)k(25m - x)^2 = mgh, where m is the mass of the jumper, g is the acceleration due to gravity, and h is the height of the jump platform (50m). Solving for x, we get x = 18.75m. Therefore, the closest distance the jumper gets to the ground is 18.75m.

It is important to note that this calculation assumes that the bungee cord follows Hooke's law, which may not be the case in real situations. Other factors such as air resistance and the weight distribution of the jumper may also affect the final distance. However, using the given information, this is the closest distance that can be calculated.