# Springs and friction and energy, etc.

1. Oct 23, 2007

1. The problem statement, all variables and given/known data
A small block of mass m is pressed up
against a spring. The spring has constant k
and is compressed a distance x. The block
slides along a track up and around a loop
of radius r and down and out on the far
side, as shown. At the top of the loop, the
loop exerts a normal force on the block
equal to the weight of the block. Neglect
friction.

Determine the compression distance, x, in terms of given quantities k, m, r and g.

2. Relevant equations

U$$_{spring}$$ = 1/2kx$$^{2}$$
KE = 1/2mv$$^{2}$$
U$$_{grav}$$ = mgh

3. The attempt at a solution

I started with energy conservation, but im not sure if you just set U$$_{spring}$$ equal to the sum of KE and U$$_{grav}$$

The picture of the problem can be seen here:

Last edited: Oct 23, 2007
2. Oct 23, 2007

### Soff

I'm not sure if I understood the problem. Why is the problem called Springs and FRICTION and energy?

You know that in the look, the gravitational potential is equal to the energy of the block. Therefore:

$$E_{kin}+m\cdot g\cdot h\cdot= U_{grav}$$

where h is equal to two times the radius r.

Now, you can set up another equation because you know that the energy of the block at the beginning was zero (no kinetic energy and no gravitational energy):

$$E_{kin}= 1/2\cdot k\cdot x^{2}$$

Now, you should know how to solve the problem...

3. Oct 23, 2007