Aim for FivePhysics 1

Mathematical routines (MR)

Block on a rough table pulled by a hanging block

  • Unit 2
  • 10 points
  • About 22 minutes

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

A multipart problem where you use math to analyze a physical situation. You draw or sketch a representation such as a free-body diagram or a graph, derive an equation using letters, calculate a numerical answer with units, and then make a claim or prediction and justify it with physics reasoning. On the exam: Question 1 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 20–25 minutes.

The question

Block A of mass m_A = 2.0 kg rests on a horizontal tabletop. A light string attached to block A passes over a light, frictionless pulley at the edge of the table and is tied to block B of mass m_B = 1.5 kg, which hangs vertically. The coefficient of kinetic friction between block A and the table is μk = 0.25. The blocks are released from rest, and block A slides toward the pulley. Use g = 9.8 m/s² (answers that use g = 10 m/s² are also accepted).

Suggested time: 22 minutes

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Part (a)

2 points

Describe the free-body diagrams for block A and for block B after the blocks are released. For each block, list every force, name the object that exerts it, and give its direction. Represent each force as a single force (no components), and state how the lengths of the arrows for block B compare.

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Part (b)

2 points

Starting with Newton's second law, derive an expression for the magnitude of the acceleration a of the blocks in terms of m_A, m_B, μk, and g, as appropriate.

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Part (c)

2 points

Calculate the magnitude of the acceleration of the blocks and the tension in the string.

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Part (d)

2 points

Block B starts 0.60 m above the floor. Calculate the speed of block B just before it hits the floor.

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Part (e)

2 points

A student claims that if the masses of both blocks are doubled, the acceleration of the blocks will double. Do you agree or disagree with the student's claim? Justify your answer.

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