Passage VII

Introduction

Students studying a unit on motion and conservation of energy were given the following information:

• Kinetic energy (energy that changes as an object's speed changes) and gravitational potential energy (energy that changes as an object's altitude changes) are forms of mechanical energy.

• An object's total mechanical energy is the sum of its kinetic energy and its gravitational potential energy.

• If an object's total mechanical energy is constant, its total mechanical energy is said to be conserved.

• Friction causes some of an object's total mechanical energy to be lost, in which case its total mechanical energy is not conserved.

The students' teacher then described the following experiment:

Suppose a student placed a block upon a surface and gave the block a single push. As the block moved along the surface, the student measured the block's speed twice in succession and found that the second measured speed was lower than the first.

Given no other information, 3 students were asked to explain the results of the 2 measurements and to predict the block's motion after the 2 measurements.

Student 1

The block was moving on a rough, horizontal surface (a surface with no incline). There was a constant frictional force between the block and the surface. This force alone caused the block to slow down at a constant rate and would have caused the block eventually to stop. Once stopped, the block would have remained at rest.

Student 2

When the 2 measurements were made, the block was moving up a frictionless, inclined surface as shown in the figure, and was slowing down at a constant rate. No air was present.

Eventually, the block would have stopped moving up the incline; then gravity alone would have caused the block to accelerate down the incline. At any specified altitude, the block's speed going down the incline would have been the same as its earlier speed going up the incline.

Student 3

The block moved on a frictionless, horizontal surface. As a result of its motion, the block encountered air resistance. Air resistance alone caused the block to slow down and lose mechanical energy. The rate at which the block slowed down depended upon the amount of air resistance it encountered. As the block's speed decreased, the amount of air resistance decreased.