# Lesson 19: Efficiency

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We do not inherit the Earth from our ancestors; we borrow it from our children.

Native American Proverb

Efficiency is a way of measuring how much of the energy that goes into doing a task is actually used to do that task. Consider a car â€“ its source of energy is the gasoline that we put into it. If the car was 100% efficient, all of that chemical energy would be converted into kinetic energy of motion used to move the car. However, not all of the energy from the gasoline goes into moving the car. Energy that is converted into forms of energy other than motion is called waste energy. In the case of the car, waste energy includes thermal energy from the heating up of the engine as well as sound energy. Neither of these forms of energy contributes to the forward motion of the car.

Thermal, or heat, energy, is generally considered a form of waste energy, and this is true unless our goal is to actually produce heat. Most forms of energy are eventually converted into thermal energy due to air resistance and friction. The application of oil to moving parts in machinery will reduce the amount of friction and therefore minimize the amount of thermal energy lost from the system. This increases the overall efficiency of the machinery.

#### Calculating Efficiency:

This concept is best illustrated with an example calculation.

#### Example 1: Efficiency When Doing Work

The work required to push a 40.0 kg ball up a 2.0 m high ramp is 1100 J. What is the efficiency of the ramp?

Given:

W_{actual }= 1100 J

m = 40.0 kg

h = 2.0 m

g = 9.8 N/kg

Required:

W_{useful }= ?

%Efficiency = ?

Solution:

W_{useful} = mghthis is considered useful work because once it is done, the energy is transformed into gravitational potential energy of the ball, a force of energy that, in turn, can be used to do work.

W_{useful} = (40.0 kg)(9.8 N/kg)(2.0 m)

W_{useful} = 784 J

The ramp is 71.3 efficient. This means that of the 1100 J of work that was done to get the ball to the top of the ramp, only 71.3% of it (784J) remains in the system and can be used to do work. The other 28.7% of the energy has now been lost from the system, primarily in the form of thermal energy that is generated due to friction.

#### Practice Questions

- Joe needs to lift a 90 kg box onto a shelf that is 1.2 m high. How much work has he done if he lifts the box straight up?
- To make the work easier, Joe decides to push the box up a 4.0 m ramp instead. To do this, he must push with a force of 300 N. How much work has he done using the ramp?
- What is the percent efficiency of the ramp?
- Where has the â€śwastedâ€ť energy gone?

**Answer**

- Given:

m =90 kg

h = 1.2 m

g = 9.8 N/kg

Required:

By lifting the box, Joe is doing work against gravity. The amount of work that he must do will equal the gravitational potential energy that he gives the box by lifting it.

W = E_{g} = ?

Solution:

W = mgh = (90 kg)(9.8 N/kg)(1.2 m) = 1060 J

- Given:

Î”d = 4.0 m

F = 300 N

Required:

W = ?

Solution:

W = FÎ”d = (300 N)(4.0 m) = 1200 J

- Given:

W_{useful} = 1060 J

W_{actual }= 1200 J

Required:

% efficiency of the ramp = ?

Solution:

- The ramp is 88.3% efficient. This means that 11.7% of the energy of the input energy is lost from the system. It is likely lost primarily as heat (thermal energy) generated due to friction.

2. Traditional incandescent light bulbs are only 2% efficient. What do you think happens to the other 98% of the energy?

**Answer**

Most of the 98% of the energy is converted to heat (thermal energy). This is why incandescent light bulbs get so hot. They are actually more efficient heaters than they are illuminators.