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# Increasing Output Distance Moved with a Lever

by Ron Kurtus (updated 3 May 2022)

You can use a Class 1 or Class 3 lever to * increase the distance* that the load moves, according to where the fulcrum is located. To increase the distance moved, the length of the load arm of the lever must be greater than the length of the effort arm.

The equation for the distance moved relates to the distance mechanical advantage of the lever. From the equation, you can determine an unknown distance or length.

Questions you may have include:

- What do the Class 1 and Class 3 levers look like?
- What is the distance relationship to the lever arms?
- What is an example of an application?

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

## Using Class 1 or Class 3 lever

You can increase the distance a load moves as compared to the distance the effort moves with either a Class 1 or a Class 3 lever.

Increase the distance the load moves with a Class 1 lever

You could use such a lever to lift a box to some that might be too high to reach. However, what you gain in distance or height requires a greater effort force. Thus in many cases, the Class 1 lever is used, because pushing down with your weight is easier than pulling up.

Increase the distance the load moves with a Class 3 lever

Since the load length (**d _{O}**) is longer for a given lever length, the Class 3 lever would have a greater distance mechanical advantage and be able to lift the object higher.

## Relationship of lever arms

When a lever rotates about its fulcrum, the input and output distances form a circular sector arc, according to the equation:

L = θ*r

where

**L**is the length of the arc**θ**is the angle of rotation (Greek letter theta)**r**is the radius

In the case of a lever, the angle **θ** is the same for both the input and output, resulting in:

D_{O}= θ*d_{O}

D_{I}= θ*d_{I}

where

**D**is the output distance that the load force is moved_{O}**D**is the input distance that the effort forces moves_{I}**d**is the length of the load or output arm_{O}**d**is the length of the effort or input arm_{I}

Distance relationship to lever arms with Class 1 lever

Since **θ = D _{O}/d_{O} = D_{I}/d_{I}**, you get the equation:

D_{O}/D_{I}= d_{O}/d_{I}

This shows that the relationship between the effort distance and load distance is dependent on the ratio of the arms of the lever.

NotethatDis also the_{O}/D_{I}distance mechanical advantageof the lever.

(See Distance Mechanical Advantage for more information.)

## Application

Suppose you wanted to lift a box to a height of 1 meter. You have a lever that is 2 meters long. You place the fulcrum at 0.5 meters from where you will apply your effort. How far do you push down? In other words, solve for **D _{I}**.

D_{O}/D_{I}= d_{O}/d_{I}

Using Algebra, rearrange the equation to get:

D_{I}= D_{O}d_{I}/d_{O}

Substitute values in this equation to find **D _{I}**:

D= 1 meter_{O}Since

d+_{O}d= 2 m,_{I}d= 0.5 m_{I}Also,

d= 2 − 0.5 = 1.5 m_{O}

Thus, the distance the effort must move is:

D= 1*(0.5)/1.5 = 0.33 m_{I}

The distance mechanical advantage of this lever is:

MA= 1/0.33 = 3_{D}= D_{O}/D_{I}

## Summary

You can use a Class 1 or Class 3 lever to increase the distance that the load moves, according to where the fulcrum is located. To increase the distance moved, the length of the load arm of the lever must be greater than the length of the effort arm.

The equation for the distance moved relates to the distance mechanical advantage of the lever.

D_{O}/D_{I}= d_{O}/d_{I}

From the equation, you can determine an unknown distance or length.

Learn from others

## Resources and references

### Websites

**Circular Sector** - Wikipedia

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## Increasing Output Distance Moved with a Lever