A small block slides along a path which is smooth until the block reaches the section of length L = 3 m , which begins at height h = 3 m on a flat incline of angle 37°, as shown in the figure. In that

Question

A small block slides along a path which is smooth until the block reaches the section of length $L = 3 m$ , which begins at height $h = 3 m$ on a flat incline of angle 37°, as shown in the figure. In that section, the coefficient of kinetic friction is 0.50 . The block passes through point A with a speed of $136 m / s$ . Find the speed (in $m / s$ ) of the block as it passes through point B where the friction ends.

path with rough incline

TestHub · Accepted Answer

From A to B the block climbs h + L sin 3 7 ∘ and friction acts over L: 2 1 ​ m v 2 = 2 1 ​ m ( 136 ) − [ m g ( h + L sin 3 7 ∘ ) + μ m g cos 3 7 ∘ L ] So v 2 = 136 − 2 [ 10 ( 3 + 3 × 0.6 ) + 0.5 × 10 × 0.8 × 3 ] = 136 − 2 [ 30 + 18 + 12 ] . Thus v 2 = 16 ⇒ v = 4 m/s .

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