1. Mechanical Advantage and Efficiency
Section 3
Mechanical Advantage
and Efficiency

2. Key Concepts
How does the actual mechanical advantage of a machine compare to its ideal mechanical advantage?
Why is the efficiency of a machine always less than 100 percent?

3. Mechanical Advantage
The mechanical advantage of a machine is the number of times that the machine increases an input force. A B
A nutcracker is a
machine capable of converting
the input force applied to it into a
larger force capable of cracking a
nut. Because it increases force,
the nutcracker has a mechanical
advantage greater than 1.

4. Actual Mechanical Advantage
The mechanical advantage determined by measuring the actual forces acting on a machine is the actual mechanical advantage.
The actual mechanical advantage (AMA) equals the ratio of the output force to the input force.
Formula:
Output force
Actual mechanical advantage =
Input force

5. Ideal Mechanical Advantage
The ideal mechanical advantage (IMA) of a machine is the mechanical advantage in the absence of friction.
Because friction is always present, the actual mechanical advantage of a machine is always less than the ideal mechanical advantage

6. Calculating Mechanical Advantage
Ideal mechanical advantage is easier to measure than actual mechanical advantage because it depends only on the locations of the forces and the distances over which they act.
Formula:
Input distance
Ideal mechanical advantage =
Output distance

7. A student working in a grocery store after school pushes several grocery carts together along a ramp. The ramp is 3 meters long and rises 0.5 meter. What is the ideal mechanical advantage of the ramp?

8. A construction worker moves a crowbar through a distance of 0
A construction worker moves a crowbar through a distance of 0.50 m to lift a load 0.05 m off of the ground. What is the IMA of the crowbar?

9. The IMA of a simple machine is 2. 5
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?

10. Efficiency
Because some of the work input to a machine is always used to overcome friction, the work output of a machine is always less than the work input.
The percentage of the work input that becomes work output is the efficiency of a machine.
Because there is always some friction, the efficiency of any machine is always less than 100 percent.
Efficiency is usually expressed as a percentage
Formula:
Work output
x 100%
Efficiency =
Work input

11. Efficiency Reducing friction increases the efficiency of a machine
The flow pattern of
a smoke trail is analyzed by
computers to determine the fluid
friction forces (air resistance)
acting on the vehicle. Engineers
use these test data to optimize a
vehicle’s shape for maximum
fuel efficiency.

12. Reviewing Concepts
1. Why is the actual mechanical advantage of a machine always less than its ideal mechanical advantage?
2. Why can no machine be 100% efficient?
3. You test a machine and find that it exerts a force of 5 N for each 1 N of force you exert operating the machine. What is the actual mechanical advantage of the machine?
4. How can two machines appear identical and yet not have the same actual mechanical advantage?
5. What information would you use to calculate the efficiency of a machine?