Any time you lift an object, you do work against gravity. We use the same formula for work that you already know (Work = force × distance), but it’s expressed in a slightly different form:
Force is written in the form mg, where m is mass and g is the acceleration due to gravity, 9.8 m/sec2. We use h for height because only the vertical distance an object moves matters for calculating work against gravity.
Did you know...If you have to lift a new sofa to a second-floor apartment, the work done against gravity is the same whether you haul it straight up the side of the building with ropes or take a longer path up the stairs. Only the vertical distance matters because the force of gravity is vertical.
You lift a 2-liter bottle of cola from a grocery bag on the floor to a refrigerator shelf that is 0.8 meter high. If the bottle has a mass of 2.02 kilograms, how much work did you do against gravity?
1. Jai-Anna, who has a mass of 45 kilograms, climbed 3 meters up a ladder to rescue her cat from a tree. How much work against gravity did she do?
2. A tram inside the Gateway Arch in Saint Louis, Missouri lifts visitors to a window-lined observation room 192 meters above the ground. How much work does the tram’s motor do against gravity to carry two 55-kilogram passengers to this room? (You may ignore the work done by the motor to carry the tram itself).
3. You pick up a 10-newton book off the floor and put it on a shelf 2 meters high. How much work did you do?
4. Elijah does 44 joules of work against gravity to pull a 0.5-kilogram rope with a 1.0-kilogram bucket attached up to the floor of his tree house. How many meters high is his tree house?
5. Alejandra weighs 225 newtons. How much work does she do against gravity when she climbs to a ledge at the top of a 15-meter climbing wall?
6. A window-washer stands on a scaffolding 30 meters above the ground. If he did 23,520 joules of work to reach the scaffolding, what is his mass?
Looking for
The amount of work done against gravity.
Solution Given
mass of bottle = 2.02 kilograms
acceleration due to gravity = 9.8 m/sec2 height = 0.8 meter
Relationship W = mgh
Work against gravity = mass acceleration due to gravity× ×height W = mgh
W = mgh
W = 2.02 kg×9.8 m/sec2×0.8 m W = 15.8 joules
Power
4.1In science, work is defined as the force needed to move an object a certain distance. The amount of work done per unit of time is called power.
Suppose you and a friend are helping a neighbor to reshingle the roof of his home. You each carry 10.0 bundles of shingles weighing 300. newtons apiece up to the roof which is 7.00 meters from the ground. You are able to carry the shingles to the roof in 10.0 minutes but your friend needs 20.0 minutes.
Both of you did the same amount of work (force × distance) but you did the work in a shorter time.
However, you had more power than your friend.
Let’s do the math to see how this is possible.
Step one: Convert minutes to seconds.
Step two: Find power.
As you can see, the same amount of work that is done in less time produces more power. You are familiar with the word watt from a light bulb. Is it now clear to you why a 100-watt bulb is more powerful than a 40-watt bulb?
W = F d×
W = 10 bundles of shingles 300 N/bundle( )×7.00 m = 21,000 joules
Power (watts) Work (joules) Time (seconds)
---=
10 minutes 60 seconds×---minute = 600 seconds (You)
20 minutes 60 seconds×---minute = 1 200 seconds (Friend),
21,000 joules 600 seconds
--- = 35 watts (You) 21,000 joules
1 200 seconds,
--- = 17.5 watts (Friend)
4.1
1. A motor does 5,000 joules of work in 20 seconds. What is the power of the motor?
2. A machine does 1,500 joules of work in 30 seconds. What is the power of this machine?
3. A hair dryer uses 72,000 joules of energy in 60 seconds. What is the power of this hair dryer?
4. A toaster oven uses 67,500 joules of energy in 45 seconds to toast a piece of bread. What is the power of the oven?
5. A horse moves a sleigh 1.00 kilometer by applying a horizontal 2,000-newton force on its harness for 45 minutes. What is the power of the horse? (Hint: Convert time to seconds.)
6. A wagon is pulled at a speed of 0.40 meters/sec by a horse exerting an 1,800-newton horizontal force. What is the power of this horse?
7. Suppose a force of 100 newtons is used to push an object a distance of 5 meters in 15 seconds. Find the work done and the power for this situation.
8. Emily’s vacuum cleaner has a power rating of 200 watts. If the vacuum cleaner does 360,000 joules of work, how long did Emily spend vacuuming?
9. Nicholas spends 20 minutes ironing shirts with his 1,800-watt iron. How many joules of energy were used by the iron? (Hint: convert time to seconds).
10. It take a clothes dryer 45 minutes to dry a load of towels. If the dryer uses 6,750,000 joules of energy to dry the towels, what is the power rating of the machine?
11. A 1000-watt microwave oven takes 90 seconds to heat a bowl of soup. How many joules of energy does it use?
12. A force of 100 newtons is used to move an object a distance of 15 meters with a power of 25 watts. Find the work done and the time it takes to do the work.
13. If a small machine does 2,500 joules of work on an object to move it a distance of 100 meters in 10 seconds, what is the force needed to do the work? What is the power of the machine doing the work?
14. A machine uses a force of 200 newtons to do 20,000 joules of work in 20 seconds. Find the distance the object moved and the power of the machine. (Hint: A joule is the same as a Newton-meter.)
15. A machine that uses 200 watts of power moves an object a distance of 15 meters in 25 seconds. Find the force needed and the work done by this machine.