Average power of a motor?

Question

How would you go about solving this problem?

"An object with a mass of 3.45 kd is pulled up a slope that is 36 meters long to a height of 3 meters. There is no friction and the acceleration is constant. The speed at the bottom of the slope is 3.5 m/s and the speed at the top of the slope is 5.5 m/s. The average power developed by the motor pulling the object is...?"

Any help is greatly appreciated.

Answer 1

The first answer ignores the kinetic energy change. The object has gained both potential and kinetic energy. ΔPE = mgh and ΔKE = (mv1^2-mv0^2)/2. Add these two changes to find the total work. Power = work/time, time = distance/average velocity, and average velocity = (v0+v1)/2.

Answer 2

average power = work / time

The work is force times distance. When the work is done only against gravity (i.e., no friction or other forces), you can take the force to be the object's weight, and the distance to be the change in height. (Or, you could also calculate the angle of the slope and figure out how hard the motor is pulling and multiply that by the length of the slope, but that would be more steps and the answer would come out the same anyway.)

work = (weight)(change in height)

Combining the two equations:

average power = (weight)(change in height) / time
(Don't forget that weight = (mass)(g))

Now you have to figure out the time. Use this equation:

time = (distance) / (average speed)

Now you have to figure out the average speed. Since the acceleration is constant, you can use this equation:

average speed = (initial speed + final speed) / 2

Now you have all the equations you need. Just apply algebra and plug in the numbers.