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Laws of Conservation

Problem 1.127

A small body of mass \(m\) is located on a horizontal plane at the point \(O .\) The body acquires a horizontal velocity \(v_{0} .\) Find: (a) the mean power developed by the friction force during the whole time of motion, if the friction coefficient \(k=0.27, m=1.0 \mathrm{~kg}\), and \(v_{0}=1.5 \mathrm{~m} / \mathrm{s}\) (b) the maximum instantaneous power developed by the friction force, if the friction coefficient varies as \(k=\alpha x,\) where \(\alpha\) is a constant, and \(x\) is the distance from the point \(O\).

Reveal Answer
 (a) ⟨P⟩=−kmgv0/2=−2 W;(b)Pmax⁡=−1/2mv02Vαg‾.\text { (a) }\langle P\rangle=-k m g v_{0} / 2=-2 \mathrm{~W} ;(b) P_{\max }=-1 / 2 m v_{0}^{2} V \overline{\alpha g} .
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