# 3.4 Power

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## Power

Performance (effort/work) is important, but the SPEED at which it is performed is also important.

## [lo 2.3; lo 2.4]

POWER = WORK / TIME

We measure this in J/s, or Watt (W)

1J per second provides 1 Watt of power

• The term Watt is derived from the name of James Watt, who was responsible for improvements to the steam engine.
• The electricity in your home is measured in kilowatt-hour (kWh) .
• One kilowatt-hour is the energy output of a 1 kW appliance in one hour.
• The longer such an appliance is operated, the more energy is used. A 2 kW heater that is operated for three hours will therefore use 6 kW energy.
• Complete: …… kW per hour x …… hour = 6 kW.
• The cost of a kWh varies but comes to approximately R0,35 in the Western Cape.

## Measure your own power capacity

• Identify a stairway in the school and measure the height of a step.
• Multiply this by the number of steps.
• Run up the stairs and take your time in seconds.

Complete the following table:

 Aspect Measurement Step height Mass Weight Work performed: F x s Time

QUESTIONS

2. Explain the following:

a) Kilowatt

b) Kilowatt-hour

3. Find out what the power rating of the average car (your educator's car, for instance) is.

4. Would you be prepared to push your educator's car all the way home? Why not?

5. Why would it be easier for the car engine to do this, even though you might have enough time and help from your friends?

6. Calculate the cost of operating a 3 000 W heater for a month (July) for 4 hours per day at a tariff of R0,35 per kWh.

Assessment of the CALCULATION of POWER CAPACITY

Were you able to apply knowledge and do the calculations?

[LO 2.3; LO 2.4]

## [lo 1.1; lo 1.2; lo 2.2; lo 2.4]

Find out what 1 kWh of electricity costs in your municipal area.

Suppose you use the following appliances during the day:

• Computer for 2 hours
• Television for 3 hours
• Lamp for 4 hours
• Kettle for 15 minutes
• Stove for 45 minutes
• Hairdryer for 15 minutes
• Determine the average power of each of these items by reading the specifications given on the appliances. Complete the table.
 Electrical appliance Power (kW) Computer Television Lamp Kettle Stove Hairdryer

Now complete the following cost assessment:

 APPLIANCE POWER (kW) as above TIME Usage(hours) Energy Usage (kW/h) Cost @ R1,50 per hour Computer Television Lamp Kettle Stove Hairdryer

QUESTIONS

2. Are you aware of the need to use energy more economically? Give your own opinion of this.

3. Calculate the following:

a) A mountaineer whose mass is 75 kg climbs a 320 m rock face in 20 minutes. Calculate his power.

b) A large cupboard weighing 150 kg has to be carried up a stairway approximately 5 m high during a move.

• How much work is performed?
• What is the performance rating of the workers if two men are able to do this in 10 minutes?

Assessment of RESEARCH on appliances

Were you able to obtain all the required information and do the calculations?

Could you categorise information?

[LO 1.1; LO 1.2; LO 2.2; LO 2.4]

## Assessment

LO 1: Scientific investigations:

The learner will be able to act confidently on curiosity about natural phenomena, and to investigate relationships and solve problems in scientific, technological and environmental contexts.

This is evident when the learner:

• plans investigations;
• conducts investigations and collects data.

LO 2: Constructing Science Knowledge:

The learner will know and be able to interpret and apply scientific, technological and environmental knowledge.

This is evident when the learner:

• categorises information;
• interprets information;

2.4 applies knowledge.

## Power

Activity

Questions:

Power = Labour (work) Time

Labour = Power (F) × s

Weight = Mass × 10 =  Kg

= F × s Time =

2. a) 1000 Watt, in other words, 1 000 × Joule/second

b) The amount of kW that is delivered or consumed in one hour

3. Larger cars approximately 100 kW; smaller cars approximately 70 kW

4. –

5. Engine has greater power / capacity for doing work

6. First calculate total consumption of energy (kWh):

= kW × h (hour)= 3 kW × 124 h= 372 Kw

Then calculate the costs:

= 372 × R0,35= R130,20

Activity

The power per hour of appliances (more of less):

• Pocket calculator 0,0006W
• Microwave oven 750W
• Drill 500W
• Toaster 800W
• Fan 100W
• Iron 1 200W
• Stove 1000W
• Computer 250W

Questions:

1. The greater the power, the higher the cost of using it

2. Debate

3. a) W = F x s= (75 x 10) x 320= 750 x 320= 240 000 J

$\begin{array}{}\text{Power}=\frac{\text{240}\text{000}J}{\left(\text{20}×\text{60}\right)}\\ =\frac{\text{240}\text{000}}{1\text{200}}\\ =\text{200}W\left(\text{or}0,2\text{lW}\right)\end{array}$

b) W = F x s = (150 x 10) x 5= 7 500 J

$\begin{array}{}\text{Drywing}=\frac{\text{Arbeid}}{\text{Tyd}}\\ =\frac{7\text{500}J}{\text{600}s}\\ =\text{12},5W\end{array}$

 One worker's performance = 12,5  2= 6,25 W

can someone help me with some logarithmic and exponential equations.
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