A massless, nonlinear spring with F s =?(40x+2x 3 ) is fixed on the left side of

Question

A massless, nonlinear spring with F s =?(40x+2x 3 ) is fixed on the left side of a level track. A block of mass m = 0.50 kg is pressed against the spring and compresses it a distance of d, as shown below. The block (initially at rest) is then released and travels toward a circular loop-the-loop of radius R = 1.5m. The entire track and the loop-the-loop are frictionless except for the section between A and B. If the coefficient of kinetic friction between the block and the track along this section is mu k =0.30 , and the length of the section is 2.5m, determine the minimum compression, d, of the spring that enables the block to just make it through the loop-the-loop at point C.

Explanation / Answer

Since we need the block to complete the loop, we require that at the highest point of the loop, the block remains "just" in contact with the loop.
In that case,
Weight of the block = Centrifugal force in it

mg = mv

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