Aim for FivePhysics 1

Translation between representations (TBR)

Block slides down a ramp onto a rough floor

  • Units 2 and 3
  • 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 2.0 kg block is released from rest at the top of a frictionless curved ramp, a vertical height h = 1.25 m above the floor. At the bottom, it slides smoothly onto a horizontal rough floor, where the coefficient of kinetic friction is μk = 0.40, and slides until it stops. Take the system to be the block, Earth, and the floor. 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)

3 points

Describe the energy bar charts you would draw for the system at three moments: (1) at release, (2) at the bottom of the ramp, and (3) after the block stops. Use the categories kinetic energy K, gravitational potential energy U_g, and thermal (internal) energy E_th, with the floor as U_g = 0.

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Part (b)

3 points

Derive an expression for the distance d the block slides on the rough floor in terms of h, μk, and physical constants, as appropriate. Then calculate d.

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Part (c)

2 points

Describe the graph of the block's kinetic energy as a function of the distance x it has traveled on the rough floor, from x = 0 until it stops. Include axes with units, the shape, and key values.

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Part (d)

2 points

Describe the graph of the block's speed as a function of time while it slides on the rough floor, from the moment it reaches the floor until it stops.

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Part (e)

2 points

A student says: "Since kinetic energy decreases linearly with distance, it must also decrease linearly with time." Do you agree or disagree? Use your graphs from parts (c) and (d) to justify your answer.

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