POWER

INTRODUCTION The amount of work you do on an object is not affected by the time it takes to do the work. For example, if you carry a backpack up a flight of stairs, the work you do is the weight of the back pack times the height of the stairs.

INTRODUCTION Whether you walk up the stairs or run up the stairs, you do the same amount of work because that is not part of the definition of work.

INTRODUCTION But time is important when you talk about power. Power is the rate at which work is done. Power equals the amount of work done on an object in a unit of time. You need more power to run up the stairs than to walk because it takes you less time to do the same work.

INTRODUCTION You and your neighbor were both snowed in during a freak blizzard in Las Vegas. You decide to shovel your sidewalk. Your neighbor has a snow blower. It takes you 30 minutes to shovel 20 feet of sidewalk. It takes your neighbor 10 minutes for the same length of sidewalk. Who did more work? Who used more power?

INTRODUCTION You did the same amount of work. Who used more power? Your neighbor did because he did the same amount of work in less time. Work is not concerned with time, but power is.

INTRODUCTION When work is measured in joules and time is measured in seconds, the SI unit for power is the joule per second (J/s). This unit is also known as the watt. One joule of work done in one second is one watt of power. So 1 J/s = 1W.

INTRODUCTION A watt is a relatively small unit of power. Because a watt is so small, it is often measured in larger units called kilowatts. 1 kilowatt is equal to 1000 watts.

INTRODUCTION When people talk about engines in vehicles, they use another measure of power called horsepower. 1 horsepower is equal to 746 watts. The unit horsepower is not an SI unit.

IN QUESTION A 60 newton rock is pulled by a 10 newton force 12 meters to the top of a 3 story building. Calculate the amount of work done in joules. 12 m x 10 N = 120 N-m = 120 J

VOCABULARY Power – amount of work done per unit of time. Watt – SI unit of power, equal to 1 J/s (joule per second)

NOTES Power needs two measurements, amount of work done and time to complete the work. power = work ÷ time. Or it can be written this way: power = (force x distance) ÷ time

NOTES Units of power: 1 watt = 1 N-m/s or 1 J/s Large amounts of power are measured in kilowatts (kW) 1 kilowatt = 1000 watts

NOTES Use the diagrams to help manipulate the formulas. W W F D P T Work = Force x Distance Power = Work ÷ Time W W F D P T

EXAMPLE 1 Calculate the power used in each example in watts: You use a force of 10 N to move a box 100 m in 10 seconds. 10 N x 100 m = 1000 N-m = 1000 J 1000 J ÷ 10 s = 100 J/s = 100 W

EXAMPLE 2 An athlete lifting weights does 900 J of work in 1 second. How much power does the weightlifter use? 900 J ÷ 1 s = 900 J/s = 900 W

EXAMPLE 3 A truck does 30,000 J of work in 15 seconds. How much power is used in kilowatts? 30,000 J ÷ 15 s = 2,000 J/s 2000 J/s = 2,000 W = 2 kW

EXAMPLE 4 A furniture mover uses a force of 150 N to move a large trunk 5 m across the floor in 10 seconds. How much power did he use? 150 N x 5 m = 750 N-m = 750 J 750 J ÷ 10 s = 75 J/s = 75 W

OUT QUESTION A large dog weighing 500 N can run a distance of 100 m in 8 seconds. Calculate the amount of power used in kilowatts. 500 N x 100 m = 50,000 J 50,000 J ÷ 8 s = 6,250 J/s = 6.25 kW