Physics and Engineering Help... If anyones out there...?

Question

For this problem he wanted us to find the formula that gives the speed of the block as a function of spring displacement. In other words.. v=v(x)where 0
A block of mass 0.80 kg is given an initial velocity v=1.2m/s to the right along a frictionless surface and collides with a spring of negligible mass and spring constant k=50 N/m . [Note. The spring is uncompressed until the block collides with it.]

the initial energy was .576 J
the final energy was the same.
The maximum x value was calculated to be x=.152 m.

Answer 1

ENergy is conserved throughout the collision with the spring. The block has initial kinetic energy K = 1/2mv0^2.

It hits the spring and starts to convert kinetic energy to potential energy stored in the spring. The spring has a potential energy U = 1/2kx^2 where x = amount of compression.

SO since energy is conserved:

K =1/2mv^2 +1/2kx^2 or

m(v0^2-v^2) = kx^2 solving for v you get

v = sqrt(v0^2 -k/m x^2)

xmax occurs when v = 0 so xmax = mv0^2/k = 0.023 m

Plot of v vs x should look like a curve starting at 1.2 m/s in y and ending at 0 at x = 0.023 m