Qualitative/quantitative translation (QQT)

Block sliding up and back down a rough ramp

Units 1 and 2
8 points
About 18 minutes

You can use a calculator on this question, just like on exam day.

A shorter multipart problem that connects reasoning in words with an equation. You make and justify a claim without equations, derive an equation from a physics principle, and then explain whether the two agree or use them to predict what happens in a changed situation. On the exam: Question 4 of 4. New for May 2027: the free-response section is 95 minutes, down from 100, for all 4 questions (50% of your score), one of each type in this order. Calculator and equation sheet allowed. The CED suggests 15–20 minutes. This question type started in May 2025, so Physics C: Mechanics free-response questions from 2024 and earlier are built differently.

The question

A block is given a quick push so that it slides up a rough ramp inclined at angle θ above the horizontal. The coefficient of kinetic friction between the block and the ramp is $\mu_k$ . The block slides up the ramp, stops momentarily, and then slides back down to its starting point. (The ramp is steep enough that the block doesn't stay at rest at the top.)

Suggested time: 18 minutes

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Part (a)

3 points

Is the time the block takes to slide up the ramp greater than, less than, or equal to the time it takes to slide back down to its starting point? Justify your answer without using equations.

Your answer to part (a)

Type math plainly, like x^2, sqrt(x) or (x+1)/(x−1).

0 / 2,500 characters

Part (b)

3 points

Derive expressions for the magnitudes of the block's acceleration on the way up, $a_{\text{up}}$ , and on the way down, $a_{\text{down}}$ . Then derive an expression for the ratio $\dfrac{t_{\text{down}}}{t_{\text{up}}}$ of the time down to the time up, in terms of θ and $\mu_k$ .

Your answer to part (b)

Type math plainly, like x^2, sqrt(x) or (x+1)/(x−1).

0 / 2,500 characters

Part (c)

2 points

Explain how your expression from part (b) supports your answer to part (a). Then use your expression to predict how the two times would compare if the ramp were frictionless, and explain why that makes sense.

Your answer to part (c)

Type math plainly, like x^2, sqrt(x) or (x+1)/(x−1).

0 / 2,500 characters

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