Can someone help me with a physics problem involving a spring, friction, and energy?

Question

A massless spring of spring constant k=78.4 N/m is fixed on the left side of a level track. A block of mass m=0.5 kg is pressed against the spring and compresses it a distance of d. The block (initially at rest) is then released and travels toward a circular loop-the-loop of radius R=1.5 m. The entire track and the loop-the-loop are frictionless except for the section of track between A and B. Given that the coefficient of kinetic friction between the block and the track along AB is u=0.30, and that the length of AB is 2.5 m, determine the minimum compression, d, of the spring that enables the block to just make it through the loop-the-loop at point C. (Hint: the force of the track on the block will be zero if the block barely makes it through the loop-the-loop).

for the diagram for this problem, please go to http://i3.photobucket.com/albums/y92/musicis4fools2/physicsdiagram.jpg

THANKS!

Answer 1

This problem can be solved with conservation of energy

First solve for the velocity of the block at the apex of the loop
using centrifugal force.
Then the potential energy of the spring
=1/2*k*d^2
will equal the loss due to friction
2.5*.3*.5*9.8
the potential energy gain to the top of the loop
.5*9.8*3
plus the kinetic energy of the block at the apex
1/2*m*g*r

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