1. Mechanical Advantage and Efficiency

2. 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.

3. Actual Mechanical Advantage
The actual mechanical advantage (AMA) equals the ratio of the output force to the input force.
AMA = Output Force / Input Force

4. 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

5. 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

6. 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 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

7. 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.

8. Efficiency We 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.

9. 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.

10. Efficiency Problems
Q: 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