# Homework Help: Springs & circular motion

1. Nov 7, 2009

### joemama69

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

A small block is launched on the fricntionless loop the loop shown. te sprink launcher has a sprink constant k

a)find the velocity at the top of the loop as a function of the displacement x of the spring launcher from its equilibrium length

b)find the minimum cvalude of x such that the block goes over the top in contact with the track

c)find the normal force on the bock A as a function of x

2. Relevant equations

3. The attempt at a solution

I believe i would have to use .5ks2, and then calculate the acceleration, and aply it to uniform circular motion, is this correct

W = .5kx2

K = .5mv2

v = (2W/m).5 = (kx2/m).5

Last edited: Nov 7, 2009
2. Nov 8, 2009

### joemama69

ok pretend my first attemp never happened

Part A
TA = .5ks2
UA = 0

TB = .5mv2
UB = -2Rmg

.5ks2 = .5mv2 - 2Rmg

v = ((ks2 + 4Rmg)/m).5

Part B

same as above, just solved for s

s = ((mv2-4Rmg)/k).5

Part C

not really sure about the Normal Force, Does it still point up even if its on the top of the loop the loop

3. Nov 8, 2009

### rl.bhat

When the block is moving in the loop, two forces are acting. One centripetal force and the other the weight of the block. Mg*cosθ contributes to the normal reaction.

4. Nov 9, 2009

### joemama69

so the normal is

N = mgcos(180)

do u agree with my other responses, they do not match what the answer is said to be

Part B answer is xmin = (5mgR/k)1/2

Part C answer is N(x) = (kx2/R) - 5mg

where does that 5 mg come from