Coefficient of Friction - F = ma | CIE A Level Maths: Mechanics Revision Notes 2020

Coefficient of Friction - F = ma

The coefficient of friction combined with F = ma allows you to determine an object's motion where friction is involved in a problem
For problems where the surface is horizontal:

Step 1. If necessary, resolve any angled forces into vertical and horizontal components

Step 2. Calculate the normal reaction force R

- Be careful – if there are vertical forces other than gravity these will affect the value of R
- with a horizontal surface R will always be directed vertically upwards
- the magnitude of R will be such as to make the total vertical force on the object zero

Step 3. Calculate F_MAX= μR and find the resultant (total force) of all the horizontal forces on the object

- Remember – if the resultant of the other horizontal forces is less than or equal to F_MAX then friction will exactly balance those forces out and the object will remain stationary

Step 4. Use F = ma to determine the acceleration of the object

3.3.3_WE_Co of Fric F-ma_1

cie-3-3-3-coefficient-of-friction---fma-worked-solution-1

Always draw a force diagram and label it clearly. Look out for the words smooth and rough in mechanics problems involving an object moving (or potentially moving) along a surface:
- If the surface is described as smooth then you can ignore friction in the problem (ie μ= 0)
- If the surface is described as rough than you need to include the force of friction in solving the problem

Be aware of whether the question is on a horizontal surface or an inclined plane.