WORK AND POWER solutions

Work is done when an object moves through a distance because of a Force acting upon the object.

• 2. When calculating work, you should use the formula: work = force X distance.

• 3. The SI unit for work is the joules. It is represented by the letter __J____.

• 4. How much work is done in holding a 15 N sack of potatoes 2m off the ground while waiting in line at the grocery store for 3 minutes?

Work = Force x DistanceW = 0 J

• 5. 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?

W = F x d

2.7 = 4.5 x d

d = 2.7/4.5 = 0.6 m

• 6. 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?

W = F x d

405 = F x 15

F = 405 / 15

F = 27 N

• 7. 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?

W = 3150 x 75.5

W = 237.825 KJ

8. 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?

W = F x d

3650 = 2470 x d

d = 3650/2470

d = 1.48 m

9. 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?

W = F x d

16700 = F x 3.05

F = 16700/3.05

F = 5475 N

10. 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?

W = F x d

W = 2000 x 150

W = 300000 J = 300 kJ

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

W = F x d

520 = F x 260

F = 2 N

• 12. A girl pushes her little brother on his sled with a force of 300. N for 750. m. How much work is this if the force of friction acting on the sled is (a) 200. N, (b) 300. N?

a. Wnet = Fnet x d

Wnet = (300 – 200) x 750

Wnet = 100 x 750

Wnet = 75000 J = 75kJ

b. Wnet = (300 – 300) x 750

Wnet = 0 J

• 13. A 75.0 kg man pushes on a 5.0 x 105 ton wall for 250 s but it does not move. How much work does he do on the wall? (2000 lb = 1 ton; 0.454 kg = 1 lb)

If the wall does not move, no work is done because d = 0 m.

• 14. A boy on a bicycle drags a wagon full of newspapers at 0.800 m/s for 30.0 min using a force of 40.0 N. How much work has the boy done?

d = v x t

d = 0.8 m/s x 30 minutes x 60 seconds/minute

d = 1440 m

W = F x d

W = 40 x 1440

W = 57600 J = 57.6 kJ

• 15. Power is the rate at which work is done.

• 16. When calculating power, you should use the formula P = work divided by time. In this formula, “P” stands for power, W stands for work, and T for time.

• 17. The SI unit for Power is the Watt(s).

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

P = W/t

W = Pt

W = 190000 x 9

W = 1710000 J = 1710 kJ

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

P = W/t

P = 250000/7.5

P = 33333 W = 33.3kW

• 20. 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?

P = W/t

t = W/P

t = 350/125

t = 2.8 seconds

• 21. A person weighing 600 N gets on an elevator. The elevator lifts the person 6 m in 10 seconds. How much power was used?

P = W/t

P = Fd/t

P = 600 x 6 / 10

P = 360 W

• 22. How much time is needed to produce 720 Joules of work if 90 watts of power is used?

P = W/t

t = W/P

t = 720/90

t = 8 seconds

• 23. A set of pulleys lifts an 800 N crate 4 meters in 7 seconds. What power was used?

P = W/t

P = Fd/t

P = 800 x 4 / 7

P = 457 W

24. A force of 5.0 N moves a 6.0 kg object along a rough floor at a constant speed of 2.5 m/s.

a. How much work is done in 25 s?

W = F x d

W = 5 x (2.5 x 25)

W = 312.5 J

b. What power is being used?

P = W/t

P = 312.5/25

P = 12.5 W

c. What force of friction is acting on the object?

constant velocity dynamic equilibrium

dynamic equilibrium equal forces

equal forces friction force equals apply force

apply force = 5 N, so friction force = 5 N

25. A car uses 2,500 Joules in 25 seconds. Find power.

P = W/t

P = 2500/25

P = 100 W

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

P = W/t

P = F x d/t

P = 30 x 10 / 5

P = 60 W

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

P = W/t

P = F x d / t

P = (30 x 9.8) x 10 / 5

P = 588 W