A block with a mass of 0.5kg is pushed against a horizontal spring of negligible mass and spring constant 450 N/m until the spring is compressed a distance x. When it is released, the block travels along a frictionless, horizontal surface to the bottom of a verticle circular track of radius 1 m, and continues to move up the track.

Question

A block with a mass of 0.5kg is pushed against a horizontal spring of negligible mass and spring constant 450 N/m until the spring is compressed a distance x. When it is released, the block travels along a frictionless, horizontal surface to the bottom of a verticle circular track of radius 1 m, and continues to move up the track. 
Determine the minimum distance the spring needs to be compressed (i.e minimum x) such that the block mass will not fall off at the top of the track.

Elena · Accepted Answer

PE (of the spring) =KE (of the block)
k•x^2/2 = m•v^2/2
v^2 = k•x/m
KE(of the block) = PE (of the block)
m•v^2/2 = m•g•h
v^2 = 2•g•h =2•g•R
k•x/m = 2•g•R
x=2•g•R•m/k =2•9.8•1•0.5/450 = 0.0218 m = 2.18 cm

natasha · Answer

hi there thanks for trying to help, although my tutor has given the answer as 0.233m. So l am therefor still puzzled by this question ... please help!!!