A block of mass m = 1 kg moving on a horizontal surface with speed u = 2 m s - 1 enters a rough horizontal patch ranging from x = 0 . 10 m to x = 2 . 00 m . If the retarding force f r on the block in this range is inversely proportional to

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A block of mass m = 1 kg moving on a horizontal surface with speed u = 2 m s - 1 enters a rough horizontal patch ranging from x = 0 . 10 m to x = 2 . 00 m . If the retarding force f r on the block in this range is inversely proportional to x over this range i.e. f r = - k x for 0 .10 < x < 2 .00 f r = 0 for x < 0.10 and x > 2.00 If k = 0 . 5 J then, the speed of this block ( in m s - 1 ) as it crosses the patch is (

Quantrex Academy · Accepted Answer

Correct answer: 1

W = ∫ f r d x = - k log e ⁡ 2 0.1 = - 1.5 J ∴ W = ∆ K 1 2 × 1 × v 2 - 1 2 × 1 × 4 = - 1.5 ⇒ v = 1 m s - 1

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