I tried to set this up however I kept getting obsene numbers and need assistance

Question

I tried to set this up however I kept getting obsene numbers and need assistance in the process of solving this problem.

A massless spring of constant k = 90.2 N/m 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 in the figure shown below. 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 points A and B. Given that the coefficient of kinetic friction between the block and the track along AB is mu k = 0.24, 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 exerted by the track on the block will be zero if the block barely makes it through the-loop-the-loop.

Explanation / Answer

at top of loop mg = mv^2/r

so v^2 = gR

conservation of energy
Ei + Wfriction = Ef

1/2 kd^2 - u m g L = m g 2 R + 1/2 mv^2
plug in v^2 = gr
1/2 kd^2 - u m g L = m g 2 R + 1/2 m g R

0.5*90.2*d^2 - 0.24*0.5*9.81*2.5 = 0.5*9.81*2*1.5 + 0.5*0.5*9.81*1.5

d=0.688 m

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