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The correct answer B shows that velocity is constant for Scenario 1. This means that, along the incline, acceleration = 0 and F_net = 0. Then, kinetic friction (Fk) and the parallel component of weight (mg sinθ) must be equal to each other to cancel out.

Fk = mg sinθ

I also learned that Fs ≤ F_applied. So, in this case, Fs ≤ mg sinθ. In other words,

Fs_max = mg sinθ

However, I also learned that kinetic friction is usually less than static friction (Fs). But, here we are getting

Fk = Fs_max = mg sinθ

I don't understand how Fk = Fs_max here. When I searched it up, I found that kinetic and static friction could be equal if their coefficients of friction are equal but that is apparently very rare. Or when the block is just starting to move. Neither of those situations applies here, I think. Did I make any mistakes in the process of getting the equations, or could Fk = Fs here?

Thanks very much! A block on an incline is initially at rest. There is nonnegligible friction between the block and the incline. In Scenario 1,the block is given a brief push at time t = 0, and begins to slide down the incline with speed v. In Scenario 2, the block is placed at the same initial position, is given a brief push at time t = 0, and begins to slide up the incline with initial speed v, as shown. The direction down the ramp corresponds to positive velocity

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I think I see what you are asking. The applied force must have been greater than $F_s$ to get the block sliding in the first place, so if the applied force is just the force due to gravity $mg\sin\theta$ we get the contradiction you describe. Or to put it another way:

If the gravitational force $mg\sin\theta$ is large enough to start the block sliding from rest then the dynamic friction cannot be large enough to make it slide at constant speed.

Your argument is correct, but the implication is that some extra external force was applied at time zero to accelerate the block to the velocity $v_0$ e.g. someone grabbed it and threw it down or up the slope. Note that the question says the block was given "a brief push" at time zero, and it is asking about the behaviour only after this external force was applied.

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