Chapter 8

Energy

The work done on an object by an applied force is the product of the force and the distance through which the object is moved.

Work = force x distance

The unit of measurement for work combines a unit of force, N, with a unit of distance m. The resulting unit of work N x m is called the joule.

“The definition of work says nothing about how long it takes to do the work. When carrying a load up some stairs, you do the same amount of work whether you walk or run up the stairs. So why are you more tired after running upstairs in a few seconds than after walking upstairs in a few minutes? To understand this difference, we need to talk about how fast work is done, or power.

Power = work donetime interval

Example:

An engine that has twice the power of another engine may not produce twice the amount of work or go twice as fast. Twice the power means that the engine can do twice the work in the same amount of time as the less powerful engine.

The watt is the unit of power or joule per second

1 kilowatt (kW) = 1000 watts

1 horsepower = .75 kW

An object may store energy by virtue of its position. Energy that is stored and held “in readiness” is called potential energy (PE).

Examples• Electrical Potential: batteries, generators• Chemical potential: energy stored in chemical bonds

between atoms in a molecule• Mechanical: stretched or compressed spring, rubber

band• Gravitational Potential Energy: amount of potential

energy possessed by an elevated object

Gravitational potential energy = weight x height

PE = mgh

• Height is the distance above some chosen reference level (i.e. the floor of a building)

Example Problems:

1. If your backpack weighs 100N and you carry it 30 meters from your classroom to your locker, how much work have you done?

Work = 100N x 30m = 3000 joules

Example Problems:

1. If your backpack weighs 100N and you carry it 8m up a flight of stairs. How much work have you done?

Work = 100N x 8m = 800 joules

2. How much gravitational potential energy has the backpack gained?

PE = mgh = 10kg x 10m/s2 x 8m = 800 joules

Example Problems:

1. If you backpack weighs 100N and you carry it 8 meters up a flight of stairs in 5 seconds, how much power did you expend?

Power = work/time interval = (100 x 8)/5 = 160 Watts

Kinetic Energy

• An object that is in motion is capable of doing work.

• kinetic energy is the energy of motion• The kinetic energy of an object depends on

the mass of the object as well as its speed• It is equal to half the mass multiplied by the

square of the speed

• KE = ½ m v2

KE = ½ mv2

• The kinetic energy of a moving object is equal to the work required to bring it to that speed from rest or, the work the object can do while being brought to rest. (Fd= Force x distance)

Fd = ½ mv2

Fd = ½ mv2

• In the above equation, note the relationship between work and energy

• If no change in energy occurs then no work is done. The same is true for potential energy.

• Whenever work is done, energy changes• This is called the work-energy theorem

Work = E

The Law of Conservation of Energy

“Energy cannot be created or destroyed. It can be transformed from one form into another, but the total amount of energy never changes.”

Machines

• A machine is device used to multiply forces or simply to change the direction of forces.

• The lever is one of the simplest machines• If we push down, the load is lifted up

Work input = work output

Since: work = force x distance

(Force x distance) input=(Force x distance)output

Mechanical Advantage

• The ratio of output force to input force for a machine is called mechanical advantage

Efficiency

• Workin = Workout

• For machines, the amount of work input equals the amount of work output, if the machine has 100% efficiency and is considered ideal

• In practice no machine converts all of the useful energy input into useful work output

Efficiency = useful work output total work input

Efficiency will always be a fraction less than 1. To convert efficiency to percent, we simply express it as a decimal and multiply by 100%

Efficiency = actual mechanical advantage theoretical mechanical advantage