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Work

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.

Power Input to a System

         

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?

A skier is pulled by a towrope up a frictionless ski slope that makes a \( 30^ \circ \) angle with the horizon. The rope moves parallel to the slope at a constant speed of \( 1 \text{ m/s}. \) The rope does \( 800 \text{ J} \) of work to the skier as the skier moves a distance of \( 8 \text{ m} \) up the incline. If instead the rope moved at a constant speed of \( 2 \text{ m/s} \), while the skier moves the same distance, with how much power would the rope do work to the skier?

A \( 4 \text{ kg} \) cactus initially at rest accelerates uniformly for \( 16\) seconds. If the cactus' speed after the acceleration is \( 16 \text{ m/s} ,\) what is the instantaneous power with which work is done to the cactus, just before the end of its acceleration?

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 \( g= 10 \text{ m/s}^2. \)

A \( 80 \text{ kg} \) block is pulled at constant speed of \( 7.0 \text{ m/s} \) across a horizontal floor by an applied force of magnitude \( 4 \text{ N} \) in a direction that makes a \( 60 ^\circ \) angle with the floor. With how much power does the force do work on the block?

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