springs & circular motion

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

joemama69

ok pretend my first attemp never happened

Part A
T_A = .5ks²
U_A = 0

T_B = .5mv²
U_B = -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

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.

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