Question

Question #c31f2

Answer 1

Gravitational potential energy is `mgh` (`g=`gravitational constant, `m=`mass and `h=`height).
Spring potential energy is `½kx^2` (`k=`spring constant, `x=`spring extension).

Explanation:

Assuming that EPE in some way stands for gravitational potential energy, we need to calculate the difference in EPE between the starting point and the end point `60-10=50`m and then the spring constant necessary to absorb this via spring potential energy.

As given above, the gravitational PE is `E_g = mgh` while the spring PE is `E_s = ½kx^2`. Therefore, taking `E_s = E_g`, we have

`" "` `mgh = ½kx^2`

Resolving for `k` we thus obtain

`" "` `k = (2mgh)/x^2`.

Moreover, we have that `h=x+l` (where `l` is the length of the cord). Therefore, with `g=10`m/s`""^2`, `h=50`m, `l=30`m and `x=h-l=20`m, we finally obtain

`" "` `k = (2\times80\times10\times50)/20^2 = 200` N/m.