Qualitative/quantitative translation (QQT)

A proton and an alpha particle crossing the same gap

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. Section II has 4 questions in 95 minutes (50% of the exam score), one of each type in this order; calculator and equation sheet allowed. The CED suggests 15–20 minutes.

The question

A proton (charge +e, mass m) and an alpha particle (charge +2e, mass 4m) are each released from rest, one at a time, next to the positive plate of a pair of large, parallel plates. Each accelerates across the gap to the negative plate. The plates are a distance d apart, the potential difference between them is ΔV, and the field between them is uniform. Gravity is negligible.

Suggested time: 18 minutes

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Part (a)

3 points

When each particle reaches the negative plate: (i) Does the alpha particle have more, less, or the same kinetic energy as the proton? (ii) Is the alpha particle's speed greater than, less than, or the same as the proton's? (iii) Does the alpha particle take more, less, or the same time to cross the gap as the proton? Justify your answers. Do not use equations in this part; reason in words.

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 (i) the ratio $\dfrac{v_\alpha}{v_p}$ of the alpha particle's final speed to the proton's, and (ii) the ratio $\dfrac{t_\alpha}{t_p}$ of the times they take to cross the gap.

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 expressions from part (b) agree with your reasoning in part (a).

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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