Power input to a system


The figure above shows constant forces F1 \vec{F_1} and F2 \vec{F_2} acting on a box as the box slides rightward across a frictionless horizontal floor. Force F1 \vec{F_1} acts horizontally leftward with a magnitude of 4 N. 4 \text{ N} . Force F2 \vec{F_2} is applied in a direction that makes a 60 60^\circ angle with the floor with a magnitude of 8 N. 8 \text{ N}. The speed v v of the box at a certain instant is 6 m/s. 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 30^ \circ angle with the horizon. The rope moves parallel to the slope at a constant speed of 1 m/s. 1 \text{ m/s}. The rope does 800 J 800 \text{ J} of work to the skier as the skier moves a distance of 8 m 8 \text{ m} up the incline. If instead the rope moved at a constant speed of 2 m/s 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 kg 4 \text{ kg} cactus initially at rest accelerates uniformly for 16 16 seconds. If the cactus' speed after the acceleration is 16 m/s, 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 kg, 1200 \text{ kg}, which is required to travel upward 18 m 18 \text{ m} in 100 100 seconds, starting and ending at rest. The elevator's counterweight has a mass of only 1000 kg, 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 m/s2. g= 10 \text{ m/s}^2.

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


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