Solve the following :


Figure (8-E7) shows a spring fixed at the bottom end of an incline of inclination $37^{\circ}$. A small block of mass $2 \mathrm{~kg}$ starts slipping down the incline from a point $4.8 \mathrm{~m}$ away from the spring. The block compresses the spring by $20 \mathrm{~cm}$, stops momentarily and then rebounds through a distance of $1 \mathrm{~m}$ up the incline. Find (a) the friction coefficient between the plane and the block and (b) the spring constant of the spring. Take $g=10 \mathrm{~m} / \mathrm{s}^{2}$.


By work energy principle

(i) for downward motion,

$0-0=(-m g \sin \theta \times s)-\mu R s-\frac{{ }^{2}}{2} k x^{2}$

$80 \mu+0.02 R=60 \ldots \ldots .(1)$

(ii) for upward motion

$0-0=(-m g \sin \theta \times s)-\mu R s+\frac{1}{2} k x^{2}$

$-16 \mu+0.02 k=12 \ldots \ldots(2)$



$k=1000 \mathrm{~N} / \mathrm{m}$

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