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?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