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# Increasing Force with a Lever

by Ron Kurtus (revised 26 September 2016)

You can use a Class 1 or Class 2 * lever* to

*pushing on the load, according to where the fulcrum is located. To increase the force on the load, the length of the effort arm of the lever must be greater than the length of the load arm.*

**increase the force**The equation for the forces relates to the work done and the distance relationships for a lever. From the equation, you can determine an unknown force or length.

Questions you may have include:

- What do the Class 1 and Class 2 levers look like?
- What is the lever force equation?
- What is an example of an application of the equation?

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

## Using Class 1 or Class 2 lever

You can use a lever to increase the applied force in order to lift a heavy load. Class 1 or Class 2 levers are used to increase the output force.

Lifting heavy load with Class 1 lever

An application of using a Class 1 lever is to lift a large rock.

Lifting heavy load with Class 2 lever

A wheelbarrow is an example of using a Class 2 lever to lift and transport a heavy load. With a wheelbarrow, the wheel acts as the fulcrum.

## Lever force equation

Assuming the resistive friction force at the fulcrum is negligible, the relationship between the input or effort and force on the load is dependent on the ratio of the arms of the lever, according to the equation:

F_{O}/F_{I}= d_{I}/d_{O}

where

**F**is the output force or the load (can also be the weight lifted)_{O}**F**is the effort or input force_{I}**d**is the length of the effort or input arm_{I}**d**is the length of the load or output arm_{O}

**Note**: **F _{O}/F_{I}** is also the

*force mechanical advantage*of the lever.

*(See Force Mechanical Advantage for more information.)*

### Derivation

The derivation of this equation starts with the fact that work is a product of the force times the distance moved or displacement:

W_{I}= F_{I}D_{I}

W_{O}= F_{O}D_{O}

where

**W**is the work done by the effort or input work_{I}**F**is the effort or input force_{I}**D**is the input distance the effort moves_{I}

and

**F**is the output force or the load (can also be the weight lifted)_{O}**D**is the output distance the load is moved_{O}**W**is the work done by the load or output work_{O}

According to the *Law of Conservation of Energy*, the output energy or work equals the input work:

W_{O}= W_{I}

Thus:

F_{O}D_{O}= F_{I}D_{I}

D_{O}/D_{I}= F_{O}/F_{I}

Applying this relationship to the distance equation (**D _{O}/D_{I} = d_{O}/d_{I}**) for levers, you get:

F_{O}/F_{I}= d_{I}/d_{O}

(See Increasing Distance Moved with a Lever for more information.)

## Application

How much effort is required to lift a load of 20 kilograms when the effort arm is 10 meters and the load arm is 1 meter?

Start by solving **F _{O}d_{O}= F_{I}d_{I}** for

**F**:

_{I}

F_{I}= F_{O}d_{O}/d_{I}

Substitute in values:

F= 20 kg_{O}

d= 0.5 m_{O}

d= 2 m_{I}

F20*(0.5)/2 = 5 kg push required to lift the 20 kg weight._{I}=

## Summary

You can use a Class 1 or Class 2 lever to increase the force pushing on the load, according to where the fulcrum is located. To increase the force on the load, the length of the effort arm of the lever must be greater than the length of the load arm.

The equation for the forces relates to the force mechanical advantage of the lever. The force equation is:

F_{O}/F_{I}= d_{I}/d_{O}

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

Set a goal to do your best

## Resources and references

### Websites

### Books

**Top-rated books on Simple Machines**

## Questions and comments

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## Increasing Force with a Lever