Question on force, kinetic friction and acceloration

[Iatro]

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Ran across this question and have no idea what the answer is.

A box that is initially at rest it pushed by a person at an angle (theta) with a force F until it reaches a speed of v. The coefficient of kinetic friction between the box is (mu). Which of the following relationships is necessarily true?

A. The work done by the person is equal in magnitude to the work done by the friction force.

B. The work done by the person is greater in magnitude than the work done by the friction force.

C. The magnitude of work done by the person is equal to the change in kinetic energy of the box.

D. The kinetic energy gained by the box is greater than the energy dissipated by friction.

Thank you in advance!!!

 

[Jkh389]

I would choose B. Because the force is being applied parallel to direction of movement, then work is being done. B is necessarily right because kinetic friction opposes direction of movement and for the object to move in the direction against friction it would be necessarily larger.

 

[Iatro]

That you so much for the response! I should have added though that there is a diagram for the problem and that the force is coming in at an angle of theta = ~ 45 degree angle, not parallel. So the guy in pushing the box into ground a little bit as well.

 

[Jkh389]

If he is pushing it up an incline plane it is still work. What I'm getting at is that it is not perpendicular to the direction of motion.

 

[medschooled]

I would also choose B. From a force perspective, only the force exerted parallel to the incline contributes to work and since the person is able to accelerate the box from 0 velocity, the force exerted must be greater than the friction force. Using the work-force relationship, given that the distance travelled is the same, B makes more sense. From an energy perspective, the person's work is changing the potential energy and the internal energy of the box whereas the friction only accounts for the internal energy.

 

[vpanopoulos]

Isn't work defined as the change in kinetic energy of an object? Work(total) = KE(final) - KE(initial)

So I would choose C.

 

[medschooled]

I think the Work-KE relationship only applies with conservative forces. In this case, there is a nonzero mu, friction should dissipate some of the energy as heat.

 

[milski]

Isn't work defined as the change in kinetic energy of an object? Work(total) = KE(final) - KE(initial)

So I would choose C.

That's true only about the total work done on the object by all forces. In this case work is being done both by the person pushing and by the gravity force. Since they are talking about the work done by the person, the answer is B.