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 FMAX= 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 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
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.
- 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.