Aim for FivePhysics C: E&M

Qualitative/quantitative translation (QQT)

Two falling loops made of thick and thin wire

  • Unit 13
  • 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

Square loops 1 and 2 have the same side length s and are made from the same metal (mass density D and resistivity ρ), but the wire of loop 2 has twice the cross-sectional area of the wire of loop 1. Each loop is held with its plane vertical, above a region of uniform horizontal magnetic field of magnitude B that points perpendicular to the plane of the loop. There is no field above the region, and the region's top edge is horizontal. Each loop is released from rest at the same height, falls with its bottom side horizontal, and reaches a constant (terminal) speed after its bottom side enters the field but before its top side does. Ignore air resistance.

Suggested time: 18 minutes

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Part (a)

3 points

Is the terminal speed of loop 2 greater than, less than, or equal to the terminal speed of loop 1? Justify your answer. Do not use equations in this part; reason in words.

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

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Part (b)

3 points

Derive an expression for the terminal speed of a loop in terms of its mass m, resistance R, s, B, and g. Then rewrite it in terms of D, ρ, B, and g, using A for the wire's cross-sectional area.

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).

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

0 / 2,500 characters

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