# External Force and Sliding Kinetic Friction

by Ron Kurtus

When an external force is applied to a sliding object in the direction of motion, the object will accelerate, move at a constant velocity, or slow down according to the sliding kinetic friction and amount of applied force.

Questions you may have include:

• What is Newton's Law for acceleration?
• What is the effect of friction on the law?
• What are the results from different external forces?

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

## Newton's Law

According to Newton's Laws, a force pushing on a freely moving object causes an acceleration according to the equation:

Fe = ma

where

• Fe is the external force on a freely moving object
• m is the mass of the object
• a is the object's acceleration

## Effect of friction

Now, if the motion of the object is sliding along a surface or material, it is held back by the resistive force of friction. The equation then becomes:

Fe − Fks = mA

or

A = (Fe − Fks)/m

where

• Fks is the kinetic sliding force of friction
• A is the new acceleration of the object relative to the external force

## Result of different external force

The relationship between the external force and the force of friction on the object determines whether it will accelerate, move at a constant velocity, or slow down.

### Accelerating

If the external force is greater than the kinetic sliding friction force (Fe > Fks), then A is positive and the object is accelerating.

Since static friction is greater than kinetic sliding friction, the object will accelerate when going from static to kinetic.

### Constant velocity

If the external force equals the kinetic sliding friction force (Fe = Fks), then A = 0 and the object is moving at a constant velocity.

This can happen by reducing the external force from the accelerating situation.

### Slowing down

If the external force is less than the kinetic sliding friction force (Fks < Ff), or if the external force equals zero (Fe = 0), then the acceleration A is negative and the object is slowing down until it finally stops moving.

A good example is when you stop sliding an object. It will start to slow down and soon stop.

## Summary

When an external force is applied to a sliding object in the direction of motion, the object will accelerate, move at a constant velocity, or slow down according to the kinetic sliding friction and amount of applied force.

## Resources and references

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