First slide
Conservation of mechanical energy
Question

In the arrangement shown, the block is released from rest from  x = 0 (when the spring was in its natural length), on an incline having µ = 0.5x. The maximum elongation in the spring will be (in m) use g=10m/s2

Moderate
Solution

Wg+Wf+WN+Wspring=ΔK 

(50sin37o)xm0xm(0.5x)(50cos37o)dx+012kxm2=12m(vf2vi2)

At the point of max. elongation v = 030xm10xm25xm2=0

30=10xm+5xm

15xm=30xm=2m

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