Mechanical Advantage and Efficiency

Mechanical Advantage

Machines can take a small input force and create a large output force.

The mechanical advantage of a machine is the number of times that the machine increases an input force.

There are two ways to calculate the mechanical advantage of a machine: actual and ideal.

Actual Mechanical Advantage

The actual mechanical advantage (AMA) equals the ratio of the output force to the input force.

AMA = Output Force / Input Force

Mechanical Advantage Problems

Q: Alex pulls on the handle of a claw hammer with a force of 15 N. If the hammer has a actual mechanical advantage of 5.2, how much force is exerted on a nail in the claw?

Q: If you exert 100 N on a jack to lift a 10,000 N car, what would be the jack’s actual mechanical advantage (AMA)

A: output force = (5.2)(15N) = 78 N

A: AMA= 10,000 N / 100 N = 100

Ideal Mechanical Advantage

The ideal mechanical advantage (IMA) is the maximum mechanical advantage a machine can have.

To have the maximum mechanical advantage, there must be no friction.

IMA = Input distance / Output distance

Mechanical Advantage Problems

Q: Calculate the ideal mechanical advantage (IMA) of a ramp that is 6.0 m long and 1.5 m high?

Q: The IMA of a simple machine is 2.5. If the output distance of the machine is 1.0 m, what is the input distance?

A: IMA = 6.0m / 1.5m = 4.0

A: Input distance = (2.5)(1.0m) = 2.5 m

AMA vs IMA

AMA is what actually happens

IMA is what could happen without friction

Since there is always some friction, AMA is less than IMA.

EfficiencyWe always want to see how efficient a

machine is.

Most cars get at least 20 miles per gallon. This is an example of efficiency.

We say that a car that gets 30 miles per gallon is more efficient.

With efficiency, we compare how much work we get from the work we put into a machine.

Efficiency

Efficiency =

(Work output / Work input) X 100%

Because there is always some friction, the efficiency of any machine is always less than 100 percent.

Efficiency ProblemsQ: Alice and Jim calculate that they must do 1800 J of

work to push a piano up a ramp. However, because they must also overcome friction, they must actually do 2400 J of work. What is the efficiency of the ramp?

Q: If the machine has an efficiency of 40%, and you do 1000 J of work on the machine, what will be the work output of the machine?

A: 1800 J/ 2400 J x 100 = 75%

A: Work Output = (Efficiency x work input) / 100% Work Output = (40% x 1000 J) / 100% = 400J