## Glossary of Work and Power

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- What takes more power, to lift an object 1 meter high in 2 minutes or in 2 seconds?
- 2 seconds - because the same amount of work is done in less time

- What is the formula for power rearranged for work?
- work = power x time

W = P x t

- If time and force remain the same, power is increased when the __________ increases. (HINT: Write the formula for power, then substitute in the formula for work. Evaluate each variable.)
- work

- What is POWER?
- The rate at which work is done, or the amount of work per unit time.

- Forty watts of power is required to do work on an object for ten seconds. How much power is required to do the same amount of work in 5 seconds?
- 80 watts

It takes twice as much power to do the same amount of work in half the time. For a given amount of work, power and time behave in opposite ways. (They have an inverse relationship. If one increases the other decreases by the same factor.For example, time was divided by two so power was multiplied by two to keep the amount of work the same.)

- For work to be done, the force applied to an object and the distance over which it acts must be in the same ______________.
- direction

- How much work is done when a 1 kg mass is raised a vertical distance of 1 meter?
- 1 joule

- What UNIT is WORK measured in?
- joule (J)

- A pulley is used to lift a 100 kg mass 5 m. How much work is done?
- W = m x g (This W is weight.)

W = 100 kg x 9.8 m/s2

W = 980 N

W = F x d (This W is work.)

W = 980 N x 5 m

W = 4,900 Nm

ANSWER: W = 4,900 J

- What is the FORMULA for WORK?
- work = force x distance

OR

W = F x d

- A 15 kg rock is lifted 4 m in 6 sec. How much power is consumed?
- W = m x g

= 15 kg x 9.8 m/s2

= 142.5 N

P = W/t = (F x d)/t

= (142.5 N x 4 m)/6 s

= 579 J / 6 s

ANSWER: 95 watts (W)

- What is WORK?
- Energy transferred through motion or a force acting through a distance.

- A teacher pushed a 12 kg desk across the floor for a distance of 10 m. She exerted a force of 45 N. How much work was done?
- W = F x d

= 45 N x 10 m

= 450 Nm

ANSWER: W = 450 J

* Note: The weight of the desk is not the resistance because an equal and opposite force is exerted on it by the floor (Newton's third law.) Instead, the teacher must overcome the inertia of the desk and friction.

- How much work is done when a crane lifts a 30,000 N object 25 m ?
- W = F x d

W = 30,000 N x 25 m

W = 750,000 Nm

ANSWER: W = 750,000 J

- A weight lifter lifts a 200 kg barbell from the floor to above his head a distance of 2.6 m. He holds the barbell for 5 s. How much work is done during the 5 second interval?
- No work is done (0 J). The barbell is not moving.

- What is the formula for power rearranged for time?
- time = work / power

t = W / P

- What are the SI UNITS of POWER?
- Watts (W)

- In terms of the SI units of force and distance, what is one joule of work equivalent to?
- One joule is the amount of work that is done in moving an object a distance of one meter with a force of one Newton.

joule = Newton x meter

(J = N x m)

- In terms of the SI units of work and time, what is one watt of power equivalent to?
- One watt is the power needed to do one joule of work in one second.

watt = joule / second

( W = J/s )

- What is the formula for work rearranged for force?
- force = work / distance

F = W / d

- A woman carries a bag of groceries home. Is work being done on the groceries? Why or why not?
- No, work is not being done on the groceries because the direction of the force on the bags is upward and the direction of motion is forward. Since theses directions are not the same, work is not being done.

- A cable car at Stone Mountain moves along an incline to transport passengers up the mountain. Is work being done if the direction of force exerted on the passengers (upward) is not the same as the direction of motion (at an incline)? Explain.
- Yes, work is being done because part of the force being applied to lift the passengers up is in the direction of motion of the car. Or, conversely, part of the displacement vector acts along the direction of force.

- If force and distance are ________________ to eachother, then no work is done.
- perpendicular

- A forklift is used to move two boxes that weigh and 20 N and 30 N, respectively, from the floor to a shelf that is 10 m high. How much work is done?
- The combined weight of the boxes is 50 N. Therefore, the forklift must apply an upward force of 50 N to overcome the downward weight of the two boxes and move them at a constant speed.

W = F x d

W = 50 N x 10 m

W = 500 Nm

ANSWER: W = 500 J

- What is the formula for work rearranged for distance?
- distance = work / force

d = W / F

- How much work is done to carry a bookbag weighing 30 N on your shoulders home a distance of 500 meters?
- None. Force and distance are not in the same direction. Because they are perpendicular to eachother, no work is being done.

- As long as part of a force acts in the direction of motion, some work is done. However, to maximize the amount of work that is done using a given force, the direction of force and the distance must be _____________ to eachother.
- parallel

- What is the FORMULA for POWER?
- power = work / time

OR

P = W / t

- A girl climbs a tree by carefully pulling herself up the trunk. Is she doing work? Why or why not?
- Yes, work is being done because the direction of force and the distance over which it acts are the same. Both are upward.

- What is the SI unit of time used to calculate power?
- seconds (s)