Aim for FivePhysics C: Mechanics

Qualitative/quantitative translation (QQT)

Sand pouring onto a moving conveyor belt

  • Units 3 and 4
  • 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

Sand falls vertically from a hopper onto a horizontal conveyor belt at a constant rate of 15 kg/s. A motor keeps the belt moving at a constant speed of 2.0 m/s. Each bit of sand lands with no horizontal velocity, slides briefly on the belt, and then moves along with it. A student claims: “The power the motor must deliver is equal to the rate at which the sand's kinetic energy increases.”

Suggested time: 18 minutes

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Part (a)

3 points

Do you agree or disagree with the student's claim? Justify your answer without using equations.

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

0 / 2,500 characters

Part (b)

3 points

Derive expressions for (i) the horizontal force the motor must exert on the belt to keep it moving at constant speed, (ii) the power the motor delivers, and (iii) the rate at which the sand's kinetic energy increases. Express each in terms of the belt speed v and the rate dmdt\dfrac{dm}{dt} at which sand lands on the belt.

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

0 / 2,500 characters

Part (c)

2 points

Explain how your expressions from part (b) support your answer to part (a). Then determine the rate at which thermal energy is produced, and explain whether that rate would change if the belt's surface were made rougher (so the sand matched the belt's speed sooner).

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

0 / 2,500 characters

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