Measuring Energy (Work) & Power: Activity; Key

Activity (Energy [as Work], Ew = F x d)

Work (J) (energy) is measured in units called joules. Work (joules) = force (newtons) x distance (metres).
  1. Calculate the work done when a 20 (newton) force moves an object 10m (metres).
    Answer: 200 joules (200 J) of work is done.

  2. Calculate the work done when a 200N force moves an object 1m.
    Answer: 200 joules (200 J) of work is done.

  3. Calculate the work done when a 25N force moves an object 100m.
    Answer: 2500 joules (2500 = 2.5kJ) of work is done.

  4. A person whose weight is 500N climbs up stairs 3m. How much work is done? How much energy is required?
    Answer: 1500 joules (1500J = 1.5kJ) of work is done. (Students might be interested to see how this compares to the energy content in various food products. The energy content of Canadian food products is usually printed on the packaging and is expressed in kilojoules per serving.)

  5. A book weighs 10N and is lifted 2m. How much work is done in lifting the book?
    Answer: 20 joules (20J) of work is done. (Note that weight is the force of gravity acting on an object and is therefore expressed in newtons ). In science mass is always in units of kilograms, and weight is always in units of newtons.

Activity (Power, P = E/t)

Power is the rate at which energy is transferred or the rate at which work is done. Work is measured in watts (W), where a watt is one joule per second.
  1. In order to do 20J (joules) of work in two seconds, what is the power required?
    Answer: 10 watts (10W) of power.

  2. In order to do 200J of work in two seconds, what is the power required?
    Answer: 100 watts (100W) of power.

  3. In order to do 2000J of work in two seconds, what is the power required?
    Answer: 1000 watts (1000W = 1kW) of power.

  4. How much power would be required for a person whose weight is 500N to run up a flight of stairs 3m high in 4 seconds?
    Answer: 1500 joules of energy expended in 4 seconds requires 375 watts (375W) of power.

  5. Your weight (in newtons) is equal to your mass (in kilograms) times 9.8. How much power would you need to run up a 3m high flight of stairs in 4 seconds?

    Answer: your mass (kilograms) x 9.8 = your weight (newtons).

    your weight (newtons) x 3 (metres) = energy needed to go up the stairs (joules)

    energy needed (joules) / 4 (seconds) = required power(watts)

Activity (Purchasing Electrical Energy, E = P x t)

Electrical energy is purchased by the kilowatt-hour rather than the joule. The price varies from a few cents per kilowatt-hour to several dollars per kilowatt hour, depending upon the production and delivery mechanisms of the electrical energy.

1 kilowatt-hour = 3.6 million joules (1kWh =3.6MJ)

To calculate the energy E consumed (in kilowatt-hours) we use E = P x t (where the power P is in watts multiplied by the time t in hours).

  1. How much energy (in kWh) is used by a 100W(watt) bulb burning for 10 hours continuously?
    Answer: 1000 watt hours or 1 kilowatt hours ( 1kWh)

  2. How much energy (in kWh) is used by a 1500W(watt) electrical heater which operates 10 hours each day?
    Answer: 15 000 watt hours or 15 kilowatt hours ( 15kWh)
    Generally watts are converted to kilowatts before multiplying by the time (in hours) so that the result is in kilowatt hours rather than watt hours.

  3. How much energy (in kWh) is used by a 1100W(watt) hair dryer used for 10 minutes each day for the month of April?
    Answer: April has 30 days, therefore 10 minutes each day adds up to 300 minutes or 5 hours.
    1.1kW x 5h equals 5.5 kilowatt hours (5.5kWh)

  4. An electric car motor is run with a power output of 30kW for 3 hours. How much energy is used?
    Answer: 90 kilowatt hours (90kWh)

  5. An electric car motor is run with a power output of 90kW for 20 minutes. How much energy is used?
    Answer: 30 kilowatt hours (30kWh)

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