# Speed Mechanical Advantage

by Ron Kurtus (28 June 2016)

A machine's speed mechanical advantage shows the effectiveness of the machine in moving an object at a greater speed than the input speed. The equation for the speed mechanical advantage is the output speed divided by the input speed.

Note: Most science books only consider force mechanical advantage. However, speed mechanical advantage is just as important.

Examples where speed mechanical advantage is employed include the catapult and bicycle.

Questions you may have include:

• What is speed mechanical advantage equation?
• What is the relationship of speed mechanical advantage and distance?
• What are some examples?

This lesson will answer those questions. Useful tool: Units Conversion

## Speed mechanical advantage equation

If you want to propel an object at a greater speed than your input motion, you would use a machine with a speed mechanical advantage. Examples are a catapult or a bicycle.

With a catapult, you push on one arm of a level and the end of the other arm moves much faster, throwing the object through the air. With a bicycle, you pedal at a certain speed, but the different sizes between the pedal sprocket and wheels and the gearing results in you going at a faster speed.

The equation for this is:

MAS = SO/SI

where

• MAS is the speed mechanical advantage
• SO is the output speed of the load
• SI is the input speed of the effort

Note: Friction in the machine does not change the ratio of the speeds.

## Relationship with distance mechanical advantage

Since distance equals speed times time, or D = St, there is a distinct relationship between speed mechanical advantage and distance mechanical advantage.

where

• MAD is the distance mechanical advantage
• DO is the output distance of the load
• DI is the input distance of the effort

DO/DI = SOt/SIt = SO/SI

Thus, Distance MA = Speed MA

## Examples

Examples include a catapult and a crank

### Catapult or lever

A catapult is used to project an object at a high speed as compared to the speed of the input or effort. It is similar to a lever with the distance from the input much shorter than the distance to the output or load. This can create a large speed mechanical advantage.

Catapult or lever increases the speed

### Crank

Turning a crank can increase the speed of the outer surface.

Crank can increase speed

## Summary

The speed mechanical advantage shows the effectiveness of the machine in moving an object at a greater speed than the input speed. The equation for the speed mechanical advantage is the output speed divided by the input speed.

MAS = SO/SI

Examples where speed mechanical advantage is employed include the catapult and crank.

Help others learn

## Resources and references

Ron Kurtus' Credentials

### Websites

The Mechanical Advantage of Machines - Carolina Curriculum (PDF)

Introduction to mechanical advantage - Khan Academy (video)

Mechanical advantage - Wikipedia

Machines Resources

### Books

(Notice: The School for Champions may earn commissions from book purchases)

## Questions and comments

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