EK 1001 Physics Question 376

[sillyjoe]

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The question reads:

A stationary 10kg box is lifted and placed at rest on top of a 10 m shelf. The move takes 2s. A student argues that the minimum average power is greater than 500W. The student is:

A. right because the box must have a change in kinetic energy in addition to the change in potential energy.
B. right because the box had to be accelerated which requires a force greater than mg.
C. wrong because the box can be moved at an infinitely slow constant velocity, and thus the work done is equal to the weight times the distance.
D. wrong because the force on the box could be twice the weight for the first half of the trip, and zero for the second half of the trip.

Answer: D

Can someone please explain this?

 

[DeathandTaxes]

F = ma, and in lifting the box, we can consider its movement going from rest to some velocity. Thus a is a nonzero value.

In this case, it must be accelerated against gravity, so the force going up must be greater than the force pushing down (mg).

 

[NextStepTutor_1]

For this question, we can calculate the power using the formula:

P = W/t = mgh/t = (10)*(10)*(10) / 2 = 500 Watts.

Thus, we can see that the minimum power is not greater than 500 watts, so the student is wrong. In that case, which of the answer choices makes the best sense?
For answer choice C, although it is true that we can apply just enough force to move the object at constant velocity, it doesn't take into account the force needed to slow the object down and then bring it to rest. Thus, we can cross this answer choice off.

The only answer choice left is answer choice D, which says that the force can be 2x weight for first half, which would accelerate the box to velocity v, and then zero for the 2nd half of the trip, which would decelerate the box back to rest. Thus, D is the correct answer choice.

 

[sillyjoe]

For this question, we can calculate the power using the formula:

P = W/t = mgh/t = (10)*(10)*(10) / 2 = 500 Watts.

Thus, we can see that the minimum power is not greater than 500 watts, so the student is wrong. In that case, which of the answer choices makes the best sense?
For answer choice C, although it is true that we can apply just enough force to move the object at constant velocity, it doesn't take into account the force needed to slow the object down and then bring it to rest. Thus, we can cross this answer choice off.

The only answer choice left is answer choice D, which says that the force can be 2x weight for first half, which would accelerate the box to velocity v, and then zero for the 2nd half of the trip, which would decelerate the box back to rest. Thus, D is the correct answer choice.

Thank you very much!