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.