Coefficient of Friction & Inclined Planes (Edexcel IAL Maths)

Coefficient of Friction - Inclined Planes

Spec point — 4.4

Coefficient of friction & inclined planes

How do I solve friction problems on 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 F_MAX= μR 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 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

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

Answer:

Exam Hint

• 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.