Coefficient of Friction - Inclined Planes (AQA A Level Maths: Mechanics)

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Coefficient of Friction - Inclined Planes

How is the coefficient of friction used in problems involving inclined planes?

  • On an inclined plane the basic principles are the same as for coefficient of friction on horizontal surfaces
  • The important directions are parallel to the plane and perpendicular to the plane (instead of horizontal and vertical)
  • Step 1. Resolve weight (and any other forces if necessary) into components parallel and perpendicular to the plane
  • Step 2. Calculate the normal reaction force R
    • Be careful – R will never simply be equal to mg in an inclined plane problem!
    • R will always be directed perpendicular to and away from the plane
    • the magnitude of R will always be such as to make the total perpendicular force zero
  • Step 3. Calculate FMAXμR and find the resultant (total force) of all the forces on the object that are parallel to the plane
    • The force of friction F will always act parallel to the plane in the direction opposite to any movement (or potential movement) of the object
    • Remember – if the resultant of the other parallel 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

Worked example

3.3.4_WE_C of F IP_1

A wooden block of mass 1 kg is released from rest on a rough plane that is inclined at 20°  above the horizontal. The coefficient of friction between the block and the plane is 0.2. Find the acceleration of the block.

aqa-3-3-4-coefficient-of-friction---inclined-planes-worked-solution1

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
  • If a friction question states that an object is on the point of moving that means that the object is in limiting equilibrium.
  • If  g = 9.8 ms-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.