Aim for FivePhysics 2

Qualitative/quantitative translation (QQT)

Energy flow through two metal rods

  • Unit 9
  • 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 2 free-response questions from 2024 and earlier are built differently.

The question

Rods X and Y are made of the same metal, and the sides of each rod are covered with insulation. Rod X has length L and radius r. Rod Y has length 2L and radius 2r. In two separate setups, one end of each rod is held in boiling water at 100°C and the other end in a mixture of ice and water at 0°C. After a while, energy flows through each rod at a steady rate.

Suggested time: 18 minutes

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Part (a)

3 points

Does energy flow into the ice–water mixture at a greater rate through rod X, at a greater rate through rod Y, or at the same rate through both? Justify your claim, addressing the effects of both the length and the radius. Do not use equations in this part; reason in words.

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

0 / 2,500 characters

Part (b)

3 points

(i) Derive an expression for the ratio PYPX\frac{P_Y}{P_X} of the rate of energy transfer through rod Y to the rate through rod X. (ii) Derive an expression for the ratio tYtX\frac{t_Y}{t_X} of the times the two rods take to transfer the same amount of energy Q to the ice–water mixture.

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

0 / 2,500 characters

Part (c)

2 points

(i) Explain how your result from part (b) agrees with your reasoning in part (a). (ii) A third rod Z of the same metal has length 2L. Predict the radius rod Z must have so that energy flows through it at the same rate as through rod X.

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

0 / 2,500 characters

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