3.3.3 Coefficient of Friction - F = ma | AQA A Level Maths: Mechanics Revision Notes 2018

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
For non-horizontal surfaces see the notes on inclined planes

3.3.3_WE_Co of Fric F-ma_1

Find the acceleration of the block.

aqa-3-3-3-coefficient-of-friction---fma-worked-solution

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.
If g = 9.8 m s^-2 has been used within a calculation then round that answer to 2 significant figures.