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Work transfers energy to a system through the forceful manipulation of its state. Do some work on yourself to master this fundamental mode of energy transfer.

The figure above shows constant forces \( \vec{F_1} \) and \( \vec{F_2} \) acting on a box as the box slides rightward across a frictionless horizontal floor. Force \( \vec{F_1} \) acts horizontally leftward with a magnitude of \( 4 \text{ N} .\) Force \( \vec{F_2} \) is applied in a direction that makes a \( 60^\circ \) angle with the floor with a magnitude of \( 8 \text{ N}. \) The speed \( v \) of the box at a certain instant is \( 6 \text{ m/s}. \) What is the net power acting on the box?

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A freight elevator is loaded with a cab with a total mass of \( 1200 \text{ kg}, \) which is required to travel upward \( 18 \text{ m} \) in \( 100 \) seconds, starting and ending at rest. The elevator's counterweight has a mass of only \( 1000 \text{ kg}, \) so the elevator motor must help. With how much power must the motor do work to the cab?

The gravitational acceleration is \( g= 10 \text{ m/s}^2. \)

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