# Rollers Reduce Friction

by Ron Kurtus (12 March 2014)

A roller is a friction-reducing machine that allows you to move a heavy object along the ground. Rolling friction is much less than sliding friction.

In order to move a heavy object along the ground, rollers can be used to reduce the resistance from friction.

A roller is a long object with a round cross-section. It must be long enough not to fall over and can easily roll along the ground or some even surface. A log or even a pencil can be used as a roller.

Usually, several rollers are used to facilitate the movement of some heavy object by reducing the resistance from friction. The force mechanical advantage of using rollers is the resistance force when dragging or sliding an object across the ground divided by the effort force when moving with the rollers

Rollers are extremely simple and a basic part of many complex machines. They were used by the ancient Egyptians in making their pyramids.

Questions you may have include:

• What is the problem when dragging an object?
• How do rollers solve the problem?
• What is the mechanical advantage of using rollers?

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

## Friction when pushing an object

Great effort is often required to push or drag a heavy object across the ground because of the resistive force of friction that must be overcome.

Friction holds back sliding a heavy object

The resistive force of friction is:

fS = μSN

where

• fS is the sliding resistive force of friction
• μS is the sliding coefficient of friction between the object and the ground (Greek letter mu)
• N is the normal force or weight of the object

Once the object is moving, the load or output force FO equals the friction force:

FO = fS

This resistive force of friction is one of the first thing ancient people wanted to overcome. In order to construct buildings they had to drag large blocks from one place to another. Friction made the job difficult.

One way to reduce friction is to lubricate the sliding surface with oil. But this was not practical in most situations. Then someone came up with the idea of placing logs or rollers under the object, so that the friction was greatly reduced.

## Solution is using rollers

A roller is a long object with a round cross-section. It must be long enough not to fall over. A log, metal rod, or even a pencil can be used as rollers. They can easily roll along the ground or some even surface.

Single roller

By placing several rollers under the object, the job of moving the object became much easier. A lever can be used to lift the object onto the rollers. Then the rollers reduce friction, and the heavy object can be easily moved from one place to another.

Rollers reduce friction and make the job easier

After hundreds of years, rollers were replaced by the invention of the wheel on an axle. A wheel is simply a refinement of the roller. These days, movers use a rack with wheels—called a dolly—to move heavy furniture.

### Friction factor

Rollers also have a resistive force due to friction, but in this case it is rolling friction. The friction is:

fR = μRN

where

• fR is the rolling resistive force of friction
• μR is the rolling coefficient of friction
• N is the normal force or weight of the object

Typically, μR is fairly small and much less that μS.

Once the object is moving, the effort force FI equals the friction force:

FR = fR

The force mechanical advantage when using rollers is the force required to slide the object along the ground divided by the force required to move the object with rollers reducing friction.

MAF = FO/FI

where

• MAF is the force mechanical advantage
• FO is the load resistance or output force required to move the object without the rollers
• FI is the effort or input force using rollers

Since FO = fS and FR = fR:

MAF = μSN/μRN

MAF = μSR

The mechanical advantage in this situation is simply the ratio of the coefficients of friction.

### Example

If the coefficient of friction for sliding a large object across the ground is μS = 0.8 and the rolling coefficient is μR = 0.01, the force mechanical advantage of using rollers is:

MAF = μSR

MAF = 0.8/0.01 = 80

Note: Distance and speed mechanical advantages don't apply in this case.

## Summary

You can use rollers to move a heavy object along the ground, since they reduce the resistance from friction. Rolling friction is much less than sliding friction.

The force mechanical advantage of using rollers is the resistance force when dragging or sliding an object across the ground divided by the effort force when moving with the rollers. Dividing the sliding coefficient of friction by the rolling coefficient is an easy way to calculate the mechanical advantage.

Be clever to solve difficult problems

## Resources and references

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