Core Unit II: Mechanical Energy
A. Work

Key Concepts

Work (W) is the product of an applied force and the displacement of an object in the direction of the applied force.

Only the component of the applied force acting in the direction of the displacement contributes to the amount of work done on an object. where is the angle between and .

The unit for work is the newton metre, N^.m. One joule (J) is the amount of work done when an applied force of one newton produces a displacement of one metre.

1 J= 1 N^.m

An alternative unit for work is the kW^.h.

1 k^.W^.h = 3.6 MJ

Work is a scalar quantity, obtained from the product of two vector quantities.

(As long as the applied force and the displacement are in the same direction, the direction can be ignored in the calculations for work. This is because the calculations yield a vector dot product. Some texts do this implicitly and omit the vector signs in the equation for work.)

Positive work is done when the applied force and the displacement act in the same direction.

Negative work is done when the applied force and the displacement act in opposite directions.

The positive work done can be combined with the negative work done, to determine the overall work done.

Work can be determined graphically by finding the area under an applied force versus displacement graph.

Energy is the ability to do work. When work is done, energy is transferred from one object to another.

An energy transformation occurs when energy is converted from one form to another.

When an energy transformation takes place, not all of the energy is used to produce useful work. Some is converted into heat or other types of energy.

Maximizing efficiency during energy transformations makes the best use of the available energy. This helps to conserve valuable resources.

Learning Outcomes

Students will increase their abilities to:

1. Define the following terms: applied force, work, energy, positive work, negative work.

2. Distinguish between positive work and negative work.

3. Recognize any of the following situations in which no work is performed on an object:
   • a force is applied but no displacement occurs,
   • the displacement acts perpendicular to an applied force,
   • an object undergoes a displacement with no applied force acting on it.

4. Determine the component of an applied force that acts in the same direction as the displacement.

5. Express the correct SI fundamental or derived units for work, energy, and various other types of physical quantities.

6. State that work is a scalar quantity.

7. Calculate work graphically from an applied force versus displacement graph.

8. Give examples to illustrate how energy is transferred from one object to another when work is done.

9. Recognize that when an energy transformation takes place, not all of the energy is used to produce useful work. Some of the energy is converted into heat or other types of energy.

10. Solve problems involving work and energy.

Teaching Suggestions, Activities and Demonstrations

1. Have the class design and perform an experiment to compare the amount of work done on an object raising it vertically and lifting it up a ramp the same vertical height.

2. Solder hooks into the inside walls near the centre of a large metal or juice container. Tie a heavy metal nut or washer to an elastic band and connect the ends of the elastic band to the hooks. Roll the container on the floor. Once the can comes to a full stop, it begins to roll back in the opposite direction. Students can try to determine where the energy came from which made the can roll in the opposite direction. Their predictions might be more interesting if the ends of the can are sealed off, so that they can not see what is inside the can.

3. Have students set up several different types of pulley systems. Perform a variety of activities to determine the applied force needed to lift several different weights at a constant velocity. Determine the input and output work. Determine the efficiency for each pulley arrangement. Discuss the idea of a mechanical advantage produced by some of the pulley systems used.