Section 8.1

Work, Power, and Machines

Objectives

• Define work and power• Calculate the work done on an object and the

rate at which work is done• Use the concept of mechanical advantage and

calculate it

Is this considered work?

Work• Definition: A quantity that measures the effects of a

force acting over a distance• Equation: W = Force * distance• W = F * d• Measured in units of Joules (J)• No force = no work– Example: A ball rolling on a flat surface at constant

velocity• No distance = no work– Example: A weightlifter holding a huge weight overhead,

but not moving it.• Force and distance must also act parallel to each other,

so is the ant actually doing any work?

Example

• A crane uses an average force of 5200 N to lift a girder 25 meters. How much work does the crane do on the girder?

• W = F * d• W = (5200 N) * (25 m)• W = 130,000 J

The definition of power?

Power

• Definition: A quantity that measures the rate at which work is done

• Equation: Power = work / time• P = W / t• Measured in units of Watts (W)• In general: Doing the same amount of work

but in less time requires more power. (running vs. walking upstairs to the 10th floor)

Example:

• A crane uses an average force of 5200 N to lift a girder 25 meters in a time of 150 seconds. Calculate the power output of the crane.

• W = F * d• W = (5200 N) * (25 m)• W = 130,000 J• P = W / t• P = (130,000 J) / (150 s)• P = 870 W

Mechanical Advantage

• Definition: A quantity that measures how much a machine multiplies force or distance

• Equation: • Mechanical advantage = output force / input force• Mechanical advantage = input distance / output distance

A mathematical example:

• W = F * d• 2 J = 2 N * 1 m• 2 J = 1 N * 2 m• 2 J = 0.5 N * 4 m• 2 J = 0.25 N * 8 m• 2 J = 0.125 N * 16 m• 2 J = 0.0625 N * 32 m

Moral of the story:• If you’re not superman, you can use mechanical advantage to lift a car by

applying small forces repeatedly over larger distances to do the same amount of work

Example:

• Determine the mechanical advantage of an automobile jack that lifts a 9900 N car with an input force of 150 N.

• Mechanical advantage = output force / input force

• Mechanical advantage = 9900 N / 150 N• Mechanical advantage = 66

Bonus: Rube-Goldberg

• Rube Goldberg device• Watch for these things:– Count how many times gravity pulls an object

downward.– Count how many times a given object is moving.– See if there are other ways in which energy is

being stored and/or released.