A 16.0kg box slides 4.0m down the frictionless ramp shown in the figure, then collides with a spring whose spring constant is 240N/m.
It is a two part question, I got neither and don't understand why.
a)What is the maximum compression of the spring?
b)At what compression of the spring does the box have its maximum speed?
See next section.
The Attempt at a Solution
For part a I did this two ways. First was to find the velocity at the spring and solve for delta s. This is what I did.
1/2mv^2 = 1/2ks^2 Solving for s using an initial velocity of 6.26 m/s I got a compressed lenght of 1.6m.
I then did it using U_g = U_sp or mgh = 1/2ks^2 which got me the same answer of 1.6m, still wrong. The correct answer is 1.98m.
The second part I thought was obvious and didn't need a forumla. I figured s soon as the mass hits the spring it is going to slow down. Because of this the max V would be the exact instant before the mass hits the spring, so I said 0cm. This turned out to the wrong as well, the correct answer being 32.7cm. This is the one I am most curious about. How isn't that zero?