Distance Mechanical Advantage
About 2 min read
A machine’s distance mechanical advantage shows the effectiveness of the machine in moving an object a greater distance than the input distance. The equation for the distance mechanical advantage is the output distance divided by the input distance.
Note: Most science books only consider force mechanical advantage. However, distance mechanical advantage is just as important.
Examples where distance mechanical advantage is employed include the lever, bicycle, and cranes.
Questions you may have include:
- What is distance mechanical advantage equation?
- How is distance mechanical advantage used with levers?
- What are other examples?
This lesson will answer those questions. Useful tool: Units Conversion
Distance mechanical advantage equation
There are times when you want to apply a force a short distance to increase the distance an object moves. The distance mechanical advantage equation is:
MAD = DO/DI
where
- MAD is the distance mechanical advantage
- DO is the distance the load moves or the output distance
- DI is the distance the effort moves or the input distance
Note that the distance directions are not taken into consideration in the mechanical advantage.
Also note: Friction in the machine does not change the distances moved.
Relationship with lever arms
The distance mechanical advantage of a lever is also a function of the distances to the lever fulcrum.
MAD = dO/dI
where
- dO is the distance of the output or load to the fulcrum
- dI is the distance of the input or effort to the fulcrum
If the input arm was dI = 0.5m and the output arm was dO = 2m, then MAD = 4.
Thus, if the input distance was DI = 3cm, then the output distance would be DO = 12cm.
Other examples
Other examples of distance mechanical advantage are a bicycle, pulley, and crane.
Bicycle
One good example is when you ride a bicycle. The distance you move the pedals on a bicycle are much less than the distance moved on the circumference of the tires.
Pulley
A pulley is an example of a machine where the output distance can be the same as the input distance, except in the opposite direction. For example, if the pulley lifted an object 1.5 meters, you would have to pull on the rope 1.5 meters, such that the mechanical advantage of the pulley would be:
MAD =1.5/1.5 = 1
Crane
Also, cranes are used to lift large items to various heights.
Summary
To move an object a greater distance than the input distance, you can calculate its distance mechanical advantage (MAD) to show the effectiveness of the machine.
The distance mechanical advantage is:
MAD = DO/DI
Examples include the lever, bicycle, pulley, and cranes.
Dream big
Resources and references
Websites
The Mechanical Advantage of Machines – Carolina Curriculum (PDF)
Introduction to mechanical advantage – Khan Academy (video)
Mechanical advantage – Wikipedia