Coefficient of Friction - F = ma (AQA A Level Maths: Mechanics)

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Coefficient of Friction - F = ma

How do we apply Newton’s Second Law (F = ma) in problems involving friction?

  • The coefficient of friction combined with 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 FMAXμR 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 FMAX 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

Worked example

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

Examiner Tip

  • 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.

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Amber

Author: Amber

Expertise: Maths

Amber gained a first class degree in Mathematics & Meteorology from the University of Reading before training to become a teacher. She is passionate about teaching, having spent 8 years teaching GCSE and A Level Mathematics both in the UK and internationally. Amber loves creating bright and informative resources to help students reach their potential.