Aim for FivePhysics 1

Translation between representations (TBR)

Riding an elevator on a bathroom scale

  • Units 1 and 2
  • 12 points
  • About 28 minutes

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

A multipart problem about one situation shown in several ways. You draw a diagram, derive equations, sketch or draw graphs, and then explain whether your answers agree with each other or use them to predict what happens when the situation changes. On the exam: Question 2 of 4. Section II has 4 questions in 95 minutes (50% of the exam score), one of each type in this order; calculator allowed. The CED suggests 25–30 minutes.

The question

A person of mass 60 kg stands on a bathroom scale on the floor of an elevator. The elevator starts at rest and moves upward in three stages: Stage 1, it speeds up uniformly from rest to 3.0 m/s in 2.0 s; Stage 2, it moves at a constant 3.0 m/s for 6.0 s; Stage 3, it slows down uniformly to rest in 3.0 s. Take upward as positive. Use g = 9.8 m/s² (answers that use g = 10 m/s² are also accepted).

Suggested time: 28 minutes

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Part (a)

2 points

Describe the free-body diagram of the person during Stage 1. List each force, name the object that exerts it, give its direction, and compare the lengths of the arrows.

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Part (b)

3 points

Derive an expression for the scale reading F_N in terms of m, g, and the person's acceleration a (with up as positive). Then calculate the scale reading during each of the three stages.

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Part (c)

3 points

Describe the graph of the scale reading as a function of time from t = 0 to t = 11 s that you would draw. Include the axes, labels with units, and the shape and values of the graph in each stage.

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Part (d)

2 points

Describe the graph of the elevator's velocity as a function of time from t = 0 to t = 11 s.

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Part (e)

2 points

Explain how your scale-reading graph from part (c) is consistent with your velocity graph from part (d). Include a quantitative check for at least one stage.

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