The 0 5lb block is pressed against a spring and released fro

The 0 5-lb block is pressed against a spring and released from rest. Ignoring friction, determine the smallest deflection of the spring such that the block will travel around the loop and just remain in contact with the loop at all times.

Solution

Here ,

k = 3 lb/in = 525.2 N/m

W = 0.5 lb = 0.227 Kg

R = 2 feet = 2 * 0.3048 m = 0.61 m

Now , speed of block needed at th top

v^2/R = g

v^2 = g * R

Now , speed u needed at the bottom

u^2 = v^2 + 2 * R * g * 2

u^2 = g * R + 4 * R *g = 5 * R * g

Using conservation of energy

0.5 * m * u^2 = 0.5 * k * x^2

0.227 * 5 * 0.61 * 9.8 = 525.2 * x^2

solving for x

x = 0.114 m

the deflection in spring needed is 0.114 m