Coefficient of Friction - F = ma (Cambridge International AS Mathematics)

Coefficient of Friction - F = ma

How do we apply Newton’s Second Law (F = ma) in problems involving friction?

• The coefficient of friction combined with **F **= ma allows you to determine an object's motion where friction is involved in a problem

• For problems where the surface is horizontal: Step 1. If necessary, resolve any angled forces into vertical and horizontal components Step 2. Calculate the normal reaction force R Step 3. Calculate F_MAX= μR and find the resultant (total force) of all the horizontal forces on the object Step 4. Use F = ma to determine the acceleration of the object

  • Be careful – if there are vertical forces other than gravity these will affect the value of R

  • with a horizontal surface R will always be directed vertically upwards

  • the magnitude of R will be such as to make the total vertical force on the object zero

  • Remember – if the resultant of the other horizontal forces is less than or equal to F_MAX then friction will exactly balance those forces out and the object will remain stationary

• For non-horizontal surfaces see the notes on inclined planes

Worked Example A wooden block of mass 2 kg is at rest on a rough horizontal floor, where the coefficient of friction between the block and the floor is 0.6. A constant force of 15 N is applied to the block at an angle of 30^o to the horizontal, as shown in the diagram below.

Find the acceleration of the block.

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

• Be aware of whether the question is on a horizontal surface or an inclined plane.