# Work and Energy with centripedal acceleration and springs.

1. Oct 6, 2008

### CaptainSFS

1. The problem statement, all variables and given/known data

The two problems below are related to a cart of mass M = 500 kg going around a circular loop-the-loop of radius R = 15 m, as shown in the figures. All surfaces are frictionless. In order for the cart to negotiate the loop safely, the normal force exerted by the track on the cart at the top of the loop must be at least equal to 0.8 times the weight of the cart. You may neglect the size of the cart. (Note: This is different from the conditions needed to "just negotiate" the loop.)

a) For this part, the cart slides down a frictionless track before encountering the loop. What is the minimum height h above the top of the loop that the cart can be released from rest in order that it safely negotiate the loop?

I found the answer to be 13.5m. I had to find velocity in the problem, which I found to be 16.275m/s.

b) For this part, we launch the cart horizontally along a surface at the same height as the bottom of the loop by releasing it from rest from a compressed spring with spring constant k = 10000 N/m. What is the minimum amount X that the spring must be compressed in order that the cart "safely" (as defined above) negotiate the loop?

This is the part I'm having trouble with.

2. Relevant equations

3. The attempt at a solution

I figured I would just set it up like I did for the first part. in the first part I used (PE) mgh = (KE) .5mv2. So instead I used the PE for springs, and set it up... .5kx2 = .5mv2. I end up dividing mv2 by k (10000), and then I take the sqrt of that to get 3.64m. This is not the correct answer, I'm doing something completely wrong. any help? thanks. :)