Force Mechanical Advantage
About 3 min read
A machine’s force mechanical advantage shows the effectiveness of the machine in providing an output force greater than the input force. The equation for the force mechanical advantage is the output force divided by the input force.
In the ideal case, there is no friction. However, the resistance from the force of friction can change the mechanical advantage.
Examples where force mechanical advantage is employed include the lever, bicycle, and cranes.
Questions you may have include:
- What is force mechanical advantage equation?
- How is force mechanical advantage used with levers?
- What about friction?
This lesson will answer those questions. Useful tool: Units Conversion
Force mechanical advantage equation
If you want to have an output force that is greater than the input or effort force, you want a machine with a good force mechanical advantage.
The force mechanical advantage equation is:
MAF = FO/FI
where
- MAF is the force mechanical advantage
- FO is the output force or load
- FI is the input force or effort required to move the object
Related to distance moved
The force mechanical advantage can also be a function of the distance moved.
MAF = DI/DO
where
- DI is the distance the effort moves or the input distance
- DO is the distance the load moves or the output distance
Application in lever
An application of force mechanical advantage equation is when you want to lift a weight or load using a lever.
Lever configuration provides force mechanical advantage
In a lever,
MAF = FO/FI
FO/FI = DI/DO = dI/dO
where
- dI is the length of the effort or input arm
- dO is the length of the load or output arm
Also:
FOdO = FIdI
Example
How much input force would be needed to move a 20 pound weight when the input arm of the lever was 4 feet and the output arm was 2 feet? What is the mechanical advantage?
Solution
Since FI = FOdO/dI then:
FI = 20*2/4 =10 pounds
MAF = FO/FI = 20/10 = 2
Affected by friction
Although resistance due to the force of friction is negliable in most levers, it can be a factor in other machines and affect the force mechanical advantage by adding to the required input force.
MA’F = FO/(FI + fr)
where
- MA’F is the force mechanical advantage with friction
- FO is the output force or load
- FI is the ideal input force or effort required to move the object
Thus, if the input force required to move an object without friction was 10 pounds, and the added friction was 2 pounds, then the new input would be have to be 10 + 2 = 12, thus reducing the mechanical advantage.
MA = (Fo – fr)/Fi
Summary
A machine’s force mechanical advantage (MAF) shows the effectiveness of the machine in providing an output force greater than the input force. The equation for the force mechanical advantage is the output force divided by the input force.
In the ideal case, there is no friction. However, the resistance from the force of friction can change the mechanical advantage. Examples where force mechanical advantage is employed include the lever, bicycle, and cranes.
Take advantage of your skills
Resources and references
Websites
The Mechanical Advantage of Machines – Carolina Curriculum (PDF)
Introduction to mechanical advantage – Khan Academy (video)
Mechanical advantage – Wikipedia