Work, Energy, and Power

Chapter 4

Work• WORK = the use of force to move an object a certain

distance.• You do work ONLY when you exert a force on an object

AND move it.• Ex: You hold a book in front of you without moving it.

This is NOT work. Moving the book up and down IS work.

• Work is done ONLY by the part of the applied force that acts in the same direction as the motion of an object.

• Moving objects can also do work.– Examples: running water, bowling balls hitting pins

Calculating Work• Work = force x distance• W = Fd• Force is measured in Newtons (N).• Distance can be measured in meters.• Work is measured in the Newton-meter (Nm) but

we call it the joule (J).• One joule is equal to the amount of work that is

done when a force of 1 Newton moves an object 1 meter.

Sample Problem• How much work is done if a person lifts a barbell

weighing 450 N to a height of 2 m?• Use KQS to solve!• What do we know? F = 450N d = 2m• What is the question? Work?• Solve! W = Fd W = 450N x 2m

W = 900 Nm 900 J

Practice Problems1. If you push a cart with a force of 70 N for 2 m, how

much work is done?

2. If you did 200 J of work pushing a box with a force of 40 N, how far did you push the box?

Energy Transfer• ENERGY = the ability of a person or an object

to do work OR cause change.• When you do work on an object, some of your

energy is transferred to that object. This is called transfer of energy, and is also measured in joules (J).

Kinetic and Potential Energy• KINETIC ENERGY = energy of motion. – Any moving object has some kinetic energy.– The faster an object moves, the more kinetic energy it

has.• POTENTIAL ENERGY = stored energy.– Example: Holding a ball above the ground.– The higher you lift it, the more work you do and the

more potential energy the ball has.• You can give objects potential energy by changing

their shape. Example: a spring

Gravitational Potential Energy• Gravitational Potential Energy = potential energy

caused by gravity• Gravitational Potential Energy = mass x gravitational

acceleration x height• GPE = mgh• g = acceleration due to earth’s gravity, = 9.8 m/s2

Sample Problem• What is the gravitational potential energy of a girl

who has a mass of 40 kg and is standing on the edge of a diving board that is 5 m above the water?

• Use KQS to solve!• What do we know? m = 40kg h = 5m• Question? What is the GPE?• Solve! GPE = mgh GPE = 40 kg x 9.8 m/s2 x

5 mGPE

= 1960 kg m2/s2

GPE = 1960 J

Practice Problems1. An apple with a mass of 0.1 kg is attached to a

branch of an apple tree 4 m from the ground. How much GPE does the apple have?

2. If you lift a 2 kg box of toys to the top shelf of a closet which is 3 m high, how much GPE will the box of toys have?

Calculating Kinetic Energy• Kinetic Energy = mass x velocity2

2• KE = ½ mv2

• Note that velocity is squared, mass is NOT!• This means increasing the velocity of an

object has a greater effect on the object’s KE than increasing the mass.

Sample Problem• What is the kinetic energy of a girl who has a mass of 40

kg and a velocity of 3 m/s?• Use KQS to solve.• K: mass = 40 kg velocity = 3 m/s• Q: kinetic energy?• S: KE = ½ mv2

KE = ½ 40kg x (3 m/s)2

KE = ½ 40 kg x 9 m2/s2 KE = ½ 360 kg x m2/s2

KE = 180 kg x m2/s2 KE = 180 J

Practice Problems1. A grasshopper with a mass of 0.002 kg jumps up at

a speed of 15 m/s. What is the KE of the grasshopper?

2. A truck with a mass of 6000 kg is traveling north on a highway at a speed of 17 m/s. A car with a mass of 2000 kg is traveling south on the same highway at a speed of 30 m/s. Which vehicle has more KE?

Mechanical Energy• MECHANICAL ENERGY (ME) = the energy an object

has due to its motion or position• The object’s combined potential energy (PE) and

kinetic energy (KE).• A thrown basketball has ME as a result of both its

motion (KE) and its PE above the ground (GPE). • Mechanical Energy = Potential Energy + Kinetic

Energy• ME = PE + KE

Calculating Mechanical Energy

• A skateboarder has a PE of 200 J due to his position at the top of a hill and a KE of 100 J due to his motion. What is his total ME?• ME = PE + KE• ME = 200 J + 100 J• ME = 300 J

Law of Conservation of Energy• Energy is transferred when work is done.• No matter how that energy is transferred or

transformed, all of the energy is still present.• This is called the Law of Conservation of Energy. As

long as you account for all forms of energy, you’ll find that the total amount of energy in a system of objects never changes.

Power• POWER = the rate at which you do work. (How

much work is done in a specific amount of time.)• If you lift a book, you do the same amount of work

whether you lift it quickly or slowly, but the faster you lift it, the more you increase your power.

• Power = Work P = Wtime t

• Work is measured in joules (J). • Power is measured in Watts (W).

Calculating Power• An Antarctic explorer uses 6000 J of work to pull his

sled for 60 s. What power does he need?• Use KQS to solve.• K: W = 6000 J t = 60 s• Q: Power?• S: P = W/t P = 6000 J/60 s P = 100 J/s

P = 100 W

Calculating Power from Energy• Sometimes you know energy is being transferred

but you can’t measure the work being done. • Ex: You know a TV uses power, but there’s no way to

measure all the work that every part of the TV does in terms of force and distance.

• So we can calculate power from energy:• Power = Energy/time P = E/t• This is just like calculating power from work, except

we are substituting in energy for the work variable.

Sample Problem• A light bulb uses 600 J of energy in 6 s. What is the

power of the light bulb?• Use KQS to solve.• K: E = 600 J t = 6 s• Q: power?• S: P = E/t P = 600 J/6 s P = 100

J/s

P = 100 W

Practice Problems1. If a conveyor belt uses 10 J to move a piece of

candy a distance of 3 m in 20 s, what is the conveyor belt’s power?

2. A laptop computer uses 100 J every 2 s. How much power is needed to run the computer?