Conceptual question concerning work and nonconservative forces

[JYZero]

Homework Statement

Hi all. I feel silly for stumbling on such a simple question, but I can't seem to wrap my head about the conceptual aspect of it. The question is: A box that is initially at rest is pushed by a person at an angle (diagonally downwards), θ, with a force, F, until it reaches a speed, v. The coefficient of kinetic friction between the box and surface is μk. Which of the following relationships is necessarily true?

a) The work done by the person is equal in magnitude to 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 the work done by the person is equal to the change in the kinetic energy of the box.
d) The kinetic energy gained by the box is greater than the energy dissipated by friction.

Homework Equations

Net work = Work done by person + Work done by friction = ΔKE

The Attempt at a Solution

When attempting to solve this problem, I got confused when rewriting the above equations, as well as whether or not there was conservation of energy here.

a) Wp + -Wf = ΔKE; This is false, as ΔKE does not equal 0.
b) Wp + -Wf = ΔKE; This is true, as ΔKE > 0.
c) Wp = ΔKE - Wf; This is false.
d) ΔKE - Wp = -Wf; This is true.

As you can see, I seem to have made an error somewhere in converting these qualitative statements into their quantitative counterparts. I know A and C are false, but B and C seem to be saying very similar things.

One last approach I used was the conservation of energy theorem, but I don't even know how to set it up right, because my book simply states it as :

Wnc = ΔKE, meaning
Wf = ΔKE

But this doesn't make sense at all, when I compare it with the original work energy theorem.

Thanks!

 

[vela]

You have it down pretty well. What you're missing is the possibility that the work done by the person and the work done by friction are pretty close. Say the person does 11 J of work and friction does -10 J. Look at (d) again with that example.

 

[JYZero]

Okay, now I see. Thinking physics in words makes things confusing sometimes, haha.

 

[vela]

One last approach I used was the conservation of energy theorem, but I don't even know how to set it up right, because my book simply states it as :

Wnc = ΔKE, meaning
Wf = ΔKE

Here, W_nc = W_p + W_f (where W_f<0). The applied force isn't a conservative force.