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, FA, is equal to the force of gravity exerted by Earth on Block B, FB. 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, FB, is greater than the force of gravity exerted by Earth on Block A, FA. 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.

15. Two new blocks, Block X and Block Y, have the same mass. Assume that the relationship between Fx and Fy is the same as the relationship stated by Student 1 between FA and FB. Consider also Student 1's statement relating the force of Earth's gravity on a block to the block's mass and its acceleration due to Earth's gravity. Will Block X have the same acceleration or a different acceleration down the incline as Block Y, and why?

Answer and Explanation

Your Answer is

Correct Answer is A

Explanation

According to student 1, FX=FY, that is, mx•ax=mY•aY and because mX=mY is given in the question stem, ax=aY is introduced