Section 8.1
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
2J=2N*1m
2J=1N*2m
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.