A block of mass m is projected with velocity v 0 over a rough surface as shown in the figure, at t = 0 . After time t 0 block stops. Consider a reference frame S , which is moving with constant ve

Question

A block of mass m is projected with velocity v 0 ​ over a rough surface as shown in the figure, at t = 0 . After time t 0 ​ block stops. Consider a reference frame S , which is moving with constant velocity v 0 ​ in the direction of motion of block, then work done by friction from t = 0 to t = t 0 ​

TestHub · Accepted Answer

(A) Ground frame: only friction works on the block: $W = Δ K = - \frac{1}{2} m v_{0}^{2}$ - correct.

(B) In S the block's velocity changes $0 \to - v_{0}$ , so $W = Δ K = + \frac{1}{2} m v_{0}^{2}$ ; S is inertial and only friction works - correct.

(C) In the ground frame the ground never moves, so friction on the ground does zero work - correct.

(D) In S the ground moves at $- v_{0}$ ; friction $μ m g$ acts for $t_{0} = v_{0} / μg$ : $W = - μ m g v_{0} t_{0} = - m v_{0}^{2} \neq = \frac{1}{2} m v_{0}^{2}$ - wrong.

Ans. (A,B,C)

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