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An electric winch pulls a 30.9 kg case of soap up a roller incline 3.01 m high in 3.15 seconds. The case starts from rest at the bottom and is moving 4.02 m/s at the top of the incline. The force of friction on the box is 39.4 N.
a) What is the increase in gravitational potential energy of the box?
b) Calculate the length of the ramp based on the average velocity and time.
c) What is the work done by friction?
d) Use the work energy theorem to find the work done by the motor.
e) What is the average horsepower produced by the motor?
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This solution contains step-by-step calculations with all formulas shown to determine variables of gravitational potential energy, length of ramp, work done by friction, work done by motor, and average horsepower.
To answer this question, we have to remember the following:
1) What is the relationship between acceleration, distance traveled, and time
2) what is work and its relationship to kinetic energy
3) What is the relationship of potential energy to work?
To answer a) a) What is the increase in gravitational potential energy of the box? We must remember that when gravity is the force acting on an object, the amount of work done by gravity (remember work is equal to the product of force times distance, where force and distance are parallel (also known as the dot product) can be stored in one of two ways. If an object has an initial velocity, and hence an initial kinetic energy, as gravity does work on the object, that energy is stored in the height of the object. Work stored in position is potential energy, and in the case of gravity, that amount of potential energy would just be:
PE = mgh.
So the amount of PE change for the box due to gravity would just be the change in height of the box times mg, or 30.9*9.81*3.01 = 912 Joules
b) Calculate the length of the ramp ...
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