Calculating Work and Power

What is work? Work is done on an object when an object moves in the same direction in which a force is applied. Force and motion must be in the same direction No work without motion!

Applying force to do work. Work is only done in direction of applied force and when object is moving. Lifting books off of desk = work by arms Carrying books to class = not work by arms but by legs

Work and Energy When you do work on an object, because it has moved, you increase its potential or kinetic energy. Potential Energy = energy of position/stored energy Height above earth Stretched rubber band Kinetic Energy = energy of motion All moving objects have kinetic energy Work = objects in motion

Examples of Work Work Is done when a force causes an object to move. Carrying books Pushing grocery cart Lifting weights Stacking blocks

Calculating Work Work = force x distance W = F x d Force is measured in Newtons Distance is measured in Meters Work is measured in Newton-meters (N·m) or Joules (J)

Calculating Work Practice Work is measured in Joules (J). Because work is the transfer of energy to an object, the Joule (J) is also the unit used to measure energy! Example: You use 42 N of force to move a couch 4m along the floor. How much work has been done? W = F x d W = 42 x 4 W = 168 J

Calculating Work What is the total amount of work done when a football player carries the ball with a force of 25 N for 50 meters?

Solution W = F x d W = 25 N x 50 m W = 1250 N x m W = 1250 J

Calculation Work A man applies a force of 500 N to push a truck 100 m down the street. How much work does he do? In which situation do you do more work? You lift a 75 N bowling ball 2 m off the floor. You lift two 50 N bowling balls 1 m off the floor.

Power-How fast work is done Power is the rate at which work is done or energy is transferred. Power = work ÷ time Power = (distance x force)/time Power is expressed in Joules per seconds, J/s or watt (W) Power is increased when more work is done in a given amount of time. Power is also increased when less time is needed to do a certain amount of work

Power Who is more powerful? A man who can lift 50 N of weight in 10 seconds or a woman who can lift 50 N of weight in 8 seconds? Woman. Same weight and work accomplished, less time.

Calculating Power Power = work/time P = w/t Watts = Joules/second What is your power if you do 200 Joules of work in 20 seconds?

P = W/t P = 200 Joules/20 seconds P = 10 Joules/sec. P = 10 Watts

Calculating Power Motor exerts a force of 12,000 N to lift an elevator 8 m in 6 seconds. What is the power produced by the motor? A crane lifts an 8,000 N beam 75 m to the top of a building in 30 seconds. How much power does the crane use?

Answers 16,000 W or 16 kW (kilowatt) 20,000 W or 20 kW (kilowatt)

Equations Summary Work = Force x Distance Power = Work ÷ Time Joules (J) = Newtons x meters Power = Work ÷ Time Watts (W) = Joules ÷ seconds

Your Turn A force of 75 N is exerted on a 45 kg couch and the couch is moved 5 m. How much work is done in moving the couch? 375 J A lawn mower is pushed with a force of 80 N. If 12,000 J of work are done in mowing a lawn, what is the total distance the lawn mower was pushed? 150 m

Your Turn The brakes on a car do 240,000 J of work in stopping the car. If the car travels a distance of 50 m while the brakes are being applied, what is the total force the brakes exert on the car? W = f x d 240,000/50 m = 4,800 N To lift a baby from a crib 50 J of work are done. How much power is needed if the baby is lifted in 0.5 s? P = W/t 50/0.5 = 100W

Your Turn If a runner’s power is 130 W, how much work is done by the runner in 10 minutes? 10 min(60 s) = 600 s P=W/t W = Pt 130 W (600 s) = 78,000 J The power produced by an electric motor is 500 W. How long will it take the motor to do 10,000 J of work? P = W/t t = W/P 10,000/500 = 20s

Work and Power Problems You use 75 N force to move your book across the table, which is a distance of 2 m. How much work has been done? If it takes you 10 sec to do 150 J of work on a box to move it up a ramp, what is your power output? A light bulb is on for 12 sec, and during that time it uses 1,200 J of electrical energy. What is the wattage (power) of the light bulb? A tow truck tows a car a distance of 40 m using a force of 500 N. How much work has been done? How much work must you do to move 100, 10 N rocks a distance of 50 meters?

Work and Power Problems 6. How far did you push the grocery cart if it required 500 Joules of work and needed 25 N of force? 7. Who has more power? Mrs. Presutti lifts 15 pieces of cake (1 piece = 1 J of work) to her mouth in 60 seconds and Mrs. Witt lifts 21 pieces of cake to her big mouth in 80 seconds. 8. What kind of energy does the cake have as it is being swallowed to the depths of Mrs. Witt’s belly? 9. What kind of energy did the cake have when it was being held high above her mouth ready to plummet to its dark grave?

Discovery Use a loop of string to attach a spring scale to a book. Slowly pull the book across a table by the spring scale. Use a stopwatch to determine the time. Record the force and time. With a ruler measure the distance you pulled the book. Now, quickly pull the book across the same distance. Record the time and force. Calculate work and power for both trials. How were the amounts of work and power affected by your pulling the book faster?

What did you discover? The amount of work done in both trials was the same. Because the work was done faster in the second trial, the power was greater.