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A2L Item 100

Meta-Information
Description: 
Identify which mass has the larger speed after a spring pushes it along a rough surface.
Goal: 
Reasoning about work and energy.
Level: 
Undergraduate
Keywords: 
Energy
Keywords: 
Friction
Keywords: 
Mechanics
Keywords: 
Springs
Keywords: 
Work
Source: 
UMPERG-ctqpe72

Consider the two situations shown above. The springs are identical and are compressed the same amount, but the masses are different with M > m. The surfaces they sit on have the same non-zero coefficient of friction. Both start from rest. Which mass has the largest speed when the spring reaches its relaxed length?

  1. m
  2. M
  3. Both have the same speed.
Commentary

Answer

(1) Friction is only a confounding element. The lighter mass will have the greater speed whether or not there is friction.

Students may correctly reason that the friction force will be less on m and less of the potential energy stored in the spring will be dissipated as the spring returns to its relaxed length. While true this is not relevant for the question.

This is an instance where it is important to elicit student reasoning. It is a case where students can use wrong reasoning to get the correct answer.