Section 2: Efficiency and Power

Name:______Date:______Period: _____ Unit 6: Work Section 2: Efficiency and Power

Learning Goals  Describe the relationship between work and power.  Apply a rule to determine the amount of power required to do work.  Explain the meaning of efficiency in terms of input and output work.

Work Input and Output Every process that is done by machines can be simplified in terms of work:

1.work input: the work or energy supplied to the process (or machine).

2.work output: the work or energy that comes out of the process (or machine).

 A rope and pulley machine illustrates a rule that is true for all processes that transform energy.

 The total energy or work output can never be greater than the total energy or work input.

Why does energy appear to be lost?

65% of the energy in gasoline is converted to heat. As far as moving the car goes, this heat energy is “lost”. The energy doesn’t vanish, it just does not appear as useful output work.

Efficiency The efficiency of a machine is the ratio of usable output work divided by total input work. Efficiency is usually expressed in percent.

Efficiency = Wo x 100% Wi

Practice Problem You see a newspaper advertisement for a new, highly efficient machine. The machine claims to produce 2,000 joules of output work for every 2,100 joules of input work. a. What is the efficiency of this machine? b. Is it as efficient as a bicycle? c. Do you believe the advertisement’s claim? Why or why not?

Looking for: efficiency of the machine

Givens: Wi = 2100 J, Wo = 2000 J

Relationship: % efficiency = Wo/Wi x 100

Solution: 2000 J / 2100 J x 100 = 95% efficiency

Power The rate at which work is done is called power. It makes a difference how fast you do work.

Example: Michael and Jim do the same amount of work. Jim’s power is greater because he gets the work done in less time.

 Power is calculated in watts.

 One watt (W) is equal to 1 joule of work per second.

 James Watt, a Scottish engineer, invented the steam engine. James Watt explained power as the number of horses his engine could replace.

 One horsepower still equals 746 watts.

Sample Problem Allen lifts his weight (500 newtons) up a staircase that is 5 meters high in 30 seconds. a. How much power does he use? b. How does his power compare with a 100-watt light bulb?

Looking for: power

Givens: Fweight= 500 N; d = 5 m, t = 30 s

Relationship: Work = F x d; Power = W ÷ t

Solution: W = 500 N x 5 m = 2500 N  m a. P = 2500 N  m ÷ 30 s = 83 watts b. Allen’s power is less than a 100-watt light bulb.

Vocabulary

2 work input – the work that is done on an object. work output – the work that an object does as a result of work input. efficiency – the ratio of usable output work divided by total input work. power – the rate of doing work or moving energy. Power is equal to energy (or work) divided by time. watt (W) – a unit of power equal to 1 joule per second. horsepower – a unit of power equal to 746 watts.

Review Questions

1. Write the equation used to calculate work efficiency. ______

2. Write the equation used to calculate power. ______

3. The total energy or work output can never be ______than the total energy or work input.

4. The ______of a machine is equal to the ratio of the work output to its input.

5. A perfect machine would have ______percent efficiency.

6. Most machines “lose” energy because of ______.

7. Power is the ______at which work is done.

8. Who was the inventor of the steam engine? ______

9. Challenge: Describe two ways that engineers can improve the efficiency of any machine.

______

Name: ______Date: ______Period: ______

Unit 6 Section 2: Efficiency and Power Calculating Efficiency Problems

In a perfect machine, the work input would equal the work output. However, there aren’t any perfect machines in our everyday world. Bicycles, washing machines, and even pencil sharpeners lose some input work to friction. Efficiency is the ratio of work output to work input. It is expressed as a percent. A perfect machine would have an efficiency of 100 percent.

Sample Problem An engineer designs a new can opener. For every twenty joules of work input, the can opener produces ten joules of work output. The engineer tries different designs and finds that her improved version produces thirteen joules of work output for the same amount of work input. How much more efficient is the new version?

Efficiency of the first design: (10 joules / 20 joules) x 100% = 50% Efficiency of the second design: (13 joules / 20 joules) x 100% = 65% The second design is 15% more efficient than the first. ______Practice Problems 1. A cell phone charger uses 4.83 joules per second when plugged into an outlet, but only 1.31 joules per second actually goes into the cell phone battery. The remaining joules are lost as heat. That’s why the battery feels warm after it has been charging for a while. How efficient is the charger?

2. A professional cyclist rides a bicycle that is 92 percent efficient. For every 100 joules of energy he exerts as input work on the pedals, how many joules of output work are used to move the bicycle?

3. An automobile engine is 15 percent efficient. How many joules of input work are required to produce 15,000 joules of output work to move the car?

4. A machine at a factory uses an average of 3500 joules a second and produces about 3000 joules of work per second. Calculate the machine’s efficiency.

5. A marathon runner ate about 5000 joules worth of food the night before a big race. The next day, the runner used about 6000 joules worth of energy in order to finish the race. How is this possible?

Name: ______Date: ______Period: ______

4 Unit 6 Section 2: Efficiency and Power Calculating Power Problems

In science, work is defined as the force needed to move an object a certain distance. The amount of work done per unit of time is called power.

Sample Problem Suppose you and a friend are helping a neighbor to reshingle the roof of his home. You each carry 10 bundles of shingles weighing 300 newtons apiece up to the roof which is 7 meters from the ground. You are able to carry the shingles to the roof in 10 minutes (600 seconds), but your friend needs 20 minutes (1,200 seconds). Both of you did the same amount of work (force × distance) but you did the work in a shorter time. Work = Force x Distance 300 N x 7 m = 21,000 joules

As you can see, more power is produced when the same amount of work is done in a shorter time period. You have probably heard the word watt used to describe a light bulb. Is it now clear to you why a 100- watt bulb is more powerful than a 40-watt bulb?

21,000 joules = 35 watts (You) 21,000 joules = 17.5 watts (Friend) 600 seconds 1, 200 seconds8.2

Practice Problems 1. A motor does 5,000 joules of work in 20 seconds. What is the power of the motor?

2. A machine does 1,500 joules of work in 30 seconds. What is the power of this machine?

3. A hair dryer uses 72,000 joules of energy in 60 seconds. What is the power of this hair dryer?

4. A toaster oven uses 67,500 joules of energy in 45 seconds to toast a piece of bread. What is the power of the oven?

5. Suppose a force of 100 newtons is used to push an object a distance of 5.0 meters in 15 seconds. Find the work done and the power for this situation.

6. Emily’s vacuum cleaner has a power rating of 200 watts. If the vacuum cleaner does 360,000 joules of work, how long did Emily spend vacuuming?