Passage III

A science teacher presents the following scenario.

Block A and Block B are released at precisely the same instant from the same starting line on a frictionless inclined plane (see the figure below).

The mass of Block A is 1 kg, and the mass of Block B is 2 kg. Earth's gravity is the only force causing the 2 blocks to accelerate down the incline. (Note: A block sliding down the incline can be considered to be falling toward Earth along the incline.)

The teacher asks 3 students to predict which block, if either, will reach the bottom of the incline first.

Student 1

The force of gravity exerted by Earth on Block A, F_A, is equal to the force of gravity exerted by Earth on Block B, F_B. Moreover, the force of gravity on a block equals the block's mass times the block's acceleration due to Earth's gravity. Thus, the mass of Block A times the acceleration of Block A must equal the mass of Block B times the acceleration of Block B. Because the mass of Block A is less than the mass of Block B, the acceleration of Block A must be greater than the acceleration of Block B. Therefore, the average speed of Block A will be greater than the average speed of Block B, so Block A will reach the bottom of the incline first.

Student 2

Because Block B has more mass than Block A, the force of gravity exerted by Earth on Block B, F_B, is greater than the force of gravity exerted by Earth on Block A, F_A. Therefore, Block B is heavier than Block A, so the acceleration of Block B will be greater than the acceleration of Block A, and Block B will slide down the incline with a greater average speed than will Block A. Thus, Block B will reach the bottom of the incline first.

Student 3

In the absence of forces other than gravity, any 2 objects falling toward Earth from the same height above Earth's surface will have the same acceleration. Because the 2 blocks will be released from the same starting line, they will be released from the same height above Earth's surface; so the blocks will slide down the incline with the same acceleration. Consequently, the 2 blocks will have the same average speed and will reach the bottom of the incline at the same time.