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A2L Item 144

Meta-Information
Description: 
Compare average speed of two masses traveling down different surfaces.
Goal: 
Reasoning with kinematics
Level: 
Undergraduate
Keywords: 
Conservation
Keywords: 
Energy
Keywords: 
Mechanics
Keywords: 
Velocity
Source: 
UMPERG-ctqpe63

Two masses, M > m, travel down the surfaces shown. Both surfaces are frictionless. Which mass has the largest average speed during their motion?

  1. m
  2. M
  3. Both have the same average speed
  4. Cannot be determined
Commentary

Answer

(1) This problem is intended to promote discussion of average speed. Both masses have the same speed at the bottom. Mass m has a larger acceleration in the beginning because the circular track is vertical at the outset. Although the angle of the incline is not specified, the angle is irrelevant. All inclines will have the same average speed. A simple graph of the speed of each mass versus time shows that m will have the larger average speed.