For the mass and pulley system shown in the figure, $F = 3 N$ and $m = 6 kg$ . The system starts from rest at $t = 0$ . Find the input power ('P' in Watts) to the system at time $t = 2 s$ . Write $\frac{P}{2}$ as your answer.

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TestHub · Accepted Answer

Two rope segments pull the 6 kg mass, each with tension F.
$ma = 2 F = 6 N$
$a = \frac{6}{6} = 1 m/ s^{2}$
At 2 s, starting from rest:
$v = a t = 2 m/s$
The free end moves at twice the mass speed:
$v_{end} = 2 v = 4 m/s$
$P = F v_{end} = 3 (4) = 12 W$
The required answer is P/2:
$\frac{P}{2} = 6$

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