Solve the following :

Question:

A small block of mass $200 \mathrm{~g}$ is kept at the top of a frictionless incline which is $10 \mathrm{~m}$ long and $3.2 \mathrm{~m}$ high. How much work was required (a) to lift the block from the ground and put it at the top, (b) to slide the block up the incline? What will be the speed of the block when it reaches the ground, if (c) it falls off the incline and drops vertically on the ground (d) it slides down the incline? Take $\mathrm{g}=10 \mathrm{~m} / \mathrm{s}^{2}$.

Solution:

(a) Work done $\mathrm{W}=\mathrm{mgh}=0.2 \times 10 \times 3.2$ (to lift the block)

$W=6.4 \mathrm{~J}$

(b) Work done $W=m g \sin \theta$ (to slide the block)

$W=6.4 \mathrm{~J}$

(c) When block falls on ground work done is

$W=\frac{1}{2} m v^{2}-0$

$6.4=\frac{1}{2} \times 0.2 \times v^{2}$

$v=8 \mathrm{~m} / \mathrm{s}$

(d) $W=\frac{1}{2} m v^{2}-0$

$6.4=\frac{1}{2} \times 0.2 \times v^{2}$

$v=8 \mathrm{~m} / \mathrm{s}$

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