Preview of Period 9: Power 9.1 Measuring the Power of Appliances How much power do appliances use? 9.2 Measuring Your Power How much power do you use for daily activities? 9.3 Measuring the Cost of Electricity How much does electricity cost? 9.4 Growth in Electricity Use How has electricity use increased over the past century? 9-1 Review of Work and Energy Work is done on an object against a force. ♦ An object is lifted against the force of gravity ♦ A box is pushed across the floor against the force of friction. W=F D Objects gain energy when work is done on them. ♦ A raised object gains gravitational potential energy. ♦ A box pushed across the floor gains kinetic energy of motion. Epot = M g h 2 Ekin = ½ M v Machines make tasks easier by reducing the force we must apply (Fin), but they cannot reduce the amount of work needed. 9-2 What is Power? Power is a rate describing the amount of work done per unit of time: Power = Work/time elapsed P = W t We can also think of power as the amount of energy transferred per unit time: Power = Energy transferred/time elapsed P = E t Power is measured in units of joules/second. One joule/second = 1 watt Power is also measured in ft-lbs/sec or horsepower (hsp). One horsepower = 746 watts One ft-lb/sec = 0.0018 hsp = 1.36 watts 9-3 Act. 9.1- 9.2: Power Requirements • Light the bulbs using power generated by your muscles. Which energy conversions take place as you crank the generator? • Do the power requirements of the appliances match their wattages? Which has the largest power requirement? • How does increasing the “load” on the drill affect its power requirement? • Time yourself climbing the stairs. How much gravitational potential energy do you gain? Calculate the power required. • How much energy is required to light the bulbs connected to the exercise bicycle? 9-4 Measuring Power with a Wattmeter 1) 2) Plug the wattmeter into the power strip and turn it on. Press the “Watt I” button. 3) Clear the meter by adjusting the Zero Adjust knob until the display reads 0 0 0. 4) Plug the appliance into the outlet in the cord attached to the wattmeter. 5) Read the power requirement. 6) Turn the meter OFF when you finish! On/Off switch 000 Zero Adjust knob Watt I Plug in appliance 9-5 Act. 9.3: The Cost of Electricity Power companies charge for electricity in units of kilowatt hours (kWh). One kilowatt hour is 1,000 watts of energy provided per hour. ♦ The energy used equals the power required by the appliance multiplied by the operating time. ♦ Find the energy used by an appliance by solving the power equation for energy, E. P = E t or E = P = power (in watts) E = energy (in joules) t = time (in seconds) P t (Example) How many kilowatt hours of energy are used when a 100 watt light bulb burns for 6½ hours? 100 watts x 1 kilowatt x 6.5 hours = 0.65 kWh 1,000 watts 9-6 Calculations with Electricity Costs Example 1: Find the total cost of electricity If electricity costs 7.5 cents/kWh, what is the cost of 0.44 kWh of electricity? 0.44 kWh x $0.075 = $0.033 kWh Example 2: Find the cost per kilowatt hour If 0.44 kWh of electricity costs 3.3 cents, what is the cost of electricity per kWh? $0.033 x 1 = 0.44 kWh $0.075 kWh Example 3: Find the kWh used. If electricity costs 7.5 cents/kWh, how many kWh can you buy for 3.3 cents? $ 0.033 x 1 kWh $0.075 = 0.44 kWh 9-7 Minimizing Electricity Costs Payback time is the time it takes to recover the additional cost of purchasing an energy efficient, more expensive appliance from the savings in energy costs. (Example 9.5) A 25 watt CF bulb costs $5 to purchase and lasts for 10,000 hours. A 75 watt incandescent bulb costs $0.50 to purchase and lasts for about 750 hours. If electricity costs $08.5/kWh, what is the cost of purchasing and operating each type of bulb for 10,000 hours? Compact Fluorescent Bulb 1. Operating cost of CF bulb: 25 watts x 1 kilowatt $0.085 x 10 ,000 hrs x 1,000 watts kilowatt hour = $21.25 2. Purchase price of CF bulb = $5.00 3. Total cost = $21.25 + $5.00 = $26.25 9-8 Minimizing Electricity Costs, Continued Incandescent Bulb 1. Operating cost of incandescent bulb: 75 watts x 2. 1 kilowatt $0.085 x 10 ,000 hrs x 1,000 watts kilowatt hour 1 bulb = 14 bulbs 750 hours Purchase price of bulbs: 14 bulbs x 4. $63.75 Number of bulbs needed for 10,000 hrs: 10 ,000 hours x 3. = $0.50 bulb = $7.00 Total cost = $63.75 + $7.00 = $70.75 Compare the cost of the two types of bulbs: Cost of Incandescent Cost of CF = $70.75 $21.25 = 3.3 Using an incandescent bulb for 10,000 hours costs 3.3 times more than using a CF bulb. 9-9 Estimated Power Requirements of Appliances Appliance Average Wattage of Appliance Annual KilowattHours Annual Cost at $0.10 per Kilowatt-Hour FOOD PREPARATION Blender Coffee Maker Dish Washer Freezer (frostless, 15 cu ft ) Frying Pan Mixer Oven, microwave Oven, self cleaning Range Refrigerator (frostless, 12 cu ft) Toaster Waste Disposal 720 900 1200 440 1200 130 1500 3000 8200 320 1100 450 15 100 360 1800 200 13 300 1100 1200 1200 40 30 $1.50 $10.00 $36.00 $180.00 $20.00 $1.30 $30.00 $110.00 $120.00 $120.00 $4.00 $3.00 5000 1000 500 2500 1000 140 100 4200 $100.00 $14.00 $10.00 $420.00 1600 200 300 170 1300 180 100 15 400 1400 150 400 140 180 160 180 27 720 $140.00 $15.00 $40.00 $14.00 $18.00 $16.00 $18.00 $2.70 $72.00 1000 14 7 14 2 5 $1.40 $0.20 $0.50 70 50 100 56 40 225 $5.60 $4.00 $22.50 LAUNDRY Clothes Dryer Iron (hand) Washing Machine Water Heater COMFORT Air Conditioner (room) Electric Blanket Dehumidifier Fan (rollaway) Heater (portable) Humidifier Lamp, Incandescent Lamp, Fluorescent Waterbed Heater HYGIENE Hair Dryer Shaver Toothbrush INFO/ENTERTAINMENT Television Stereo Personal Computer Act. 9.4: Growth Rates Linear Growth ♦ Linear growth is constant. straight line. Its graph is a ♦ The same amount is added during each time period. ♦ The amount added is independent of the initial amount. ♦ The amount added is independent of the number of elapsed time periods. Exponential Growth ♦ Exponential growth is not constant. Its graph is an upward curving line. ♦ The amount added changes with each time period. ♦ Exponential growth doubles the amount of the quantity during each time period. ♦ The amount added depends on the initial amount and on the number of time periods. ♦ The doubling time is the length of time required for the quantity to double. 9-10 Act. 9.4: Growth Rates Electricity Production in the U.S. 3000 2500 2000 1500 1000 500 1995 1990 1985 1980 1975 1970 1965 1960 1955 1950 1945 1940 1935 0 1930 Kilowatt Hours (billions) 3500 9-11 Period 9 Summary 9.1:Power is the rate at which work is done or energy is transferred. P = W/t or P = E/t Power is measured in joules/second, or watts, in metric units and in ft-lbs/second or horsepower in English units. 9.2:Electrical energy provided to homes is measured and billed in kilowatt hours. 9.3:Payback time is the time it takes to recover the additional cost of purchasing an energy efficient, more expensive appliance from the savings in energy costs. 9-12 Period 9 Summary, Continued 9.4:Electricity production in the U.S. has grown rapidly – at times linearly and at other times exponentially. ♦ Linear growth adds a constant amount to the initial amount each time period. ♦ Linear growth rates are independent of the initial amount and the number of time periods. ♦ Exponential growth doubles the amount each time period. ♦ Exponential growth rates are dependent on the initial amount and on the number of time periods elapsed. ♦ The time needed to double a quantity is called its doubling time. 9-13 Period 9 Review Questions R.1 What is power? equations. Give a definition and R.2 Which of the following appliances would be likely to use the most power per year: microwave oven, washing machine, refrigerator, toaster, or range? R.3 What is a kilowatt-hour? What quantity does the electric company bill you for – power, energy, or some other quantity? R.4 How could it be profitable for a power company to encourage customers to use less electricity? R.5 How can you determine whether a graph is increasing linearly or exponentially? 9-14

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