Work and Power

When a force acts upon an object to cause a displacement of the object, it is said that work was done upon the object. There are three key ingredients to work - force, distance, and cause. In order for a force to qualify as having done work on an object, there must be a distance and the force must cause the displacement. There are several good examples of work that can be observed in everyday life - a horse pulling a plow through the field, a father pushing a grocery cart down the aisle of a grocery store, a freshman lifting a backpack full of books upon her shoulder, a weightlifter lifting a barbell above his head, an Olympian launching the shot-put, etc. In each case described here there is a force exerted upon an object to cause that object to be displaced.

Work is done on an object if a force is applied and the object moves in the direction in which force is applied.

 

 

Mathematically, work can be expressed by the following equation.

W=F*d

where

W is work

F is the force,

d is the distance

Units of Work

Whenever a new quantity is introduced in physics, the standard metric units associated with that quantity are discussed. In the case of work (and also energy), the standard metric unit is the Joule (abbreviated J). One Joule is equivalent to one Newton of force causing a displacement of one meter. In other words,

The Joule is the unit of work.

1 Joule = 1 Newton * 1 meter

1 J = 1 N * m

 

Power

Sometimes, the work is done very quickly and other times the work is done rather slowly. For example, a rock climber takes an abnormally long time to elevate her body up a few meters along the side of a cliff. On the other hand, a trail hiker (who selects the easier path up the mountain) might elevate her body a few meters in a short amount of time. The two people might do the same amount of work, yet the hiker does the work in considerably less time than the rock climber. The quantity that has to do with the rate at which a certain amount of work is done is known as the power. The hiker has a greater power rating than the rock climber.

Power is the rate at which work is done. It is the work/time ratio. Mathematically, it is computed using the following equation.

P=W/t

where

P is power

W is watt

t is time

The standard metric unit of power is the Watt. As is implied by the equation for power, a unit of power is equivalent to a unit of work divided by a unit of time. Thus, a Watt is equivalent to a Joule/second. 

Solve the following problems. REMEMBER YOU MUST SHOW ALL YOUR WORK

1. How much work is done by a crane that lowers 1,000 newtons of material a distance of 150 meters?

2. How much work is done when a 1 kilogram mass is raised a vertical distance of 1 meter?

3. A 49 newton rock is lifted 2 meters in 5 seconds.

a. How much work is done?

b. What power is used?

4. A student who weighs 500 newtons climbed the stairs from the first floor to the third floor, 15 meters above, in 20 seconds.

a. How much work did she do?

b. What was her power?


5. A box is pushed across the floor for a distance of 5 meters with a force of 50 newtons in 5 seconds.

a. How much work is done?


b. What is the power?

6. A woman lifts a 300 newton child a distance of 1.5 meters in 0.75 seconds. What is her power output in lifting the child?

7. Calculate the work done by a 47 N force pushing a pencil 0.26 m.

8.  Calculate the work done by a 47 N force pushing a 0.025 kg pencil 0.25 m against a force of 23 N.

9. Calculate the work done by a 2.4 N force pushing a 400. g sandwich across a table 0.75 m wide.

10. How much work is it to lift a 20. kg sack of potatoes vertically 6.5 m? Acceleration 9.8m/s²

11.  If a small motor does 520 J of work to move a toy car 260 m, what force does it exert?

12.  A girl pushes her little brother on his sled with a force of 300 N for 750 m.  How much work is done?

a. How much power does it take to lift 30.0 N 10.0 m high in 5.00 s?

13.  How much power does it take to lift 30.0 kg 10.0 m high in 5.00 s?

14. Indicate whether or not the following represent examples of work. Explain your answer.

	Work done
A teacher applies a force to a wall and becomes exhausted. Explanation:	Yes or No?
b. A weightlifter lifts a barbell above her head. Explanation:	Yes or No?
c. A waiter carries a tray full of meals across a dining room at a constant speed. Explanation:	Yes or No?
d. A rolling marble hits a note card and moves it across a table. Explanation:	Yes or No?
e. A shot-putter launches the shot. Explanation:	Yes or No?

15. You must exert a force of 4.5 N on a book to slide it across a table. If you do 2.7 J of work in the process, how far have you moved the book?

16. A child pulls a sled up a snow-covered hill. The child does 405 J of work on the sled. If the child walks 15 m up the hill, how large of a force must the child exert?

17. How much work is done on a small car if a 3150 N force is exerted to move it 75.5 m to the side of the road?

18. A crate is being lifted into a truck. If it is moved with a 2470 N force and 3650 J of work is done, then how far is the crate being lifted?

19. If 16,700 J of work is done to shoot the human cannonball down a 3.05 m barrel, then how much force is applied to the person to fire them out the cannon?

20. An elephant pushes with 2000 N on a load of trees. It then pushes these trees for 150 m. How much work did the elephant do?

21.  An 190,000 W engine can accelerate from rest to a top speed in 9 s. How much work did the engine do?

22. Another engine reaches its top speed from rest in 7.5 s. It is able to perform 250,000 J of wok in that time. How much power does this engine have in that time?

23. If a runner exerts 350 J of work to make 125 W of power, then how long did it take the runner to do the work?