CIE A Level Maths: Mechanics复习笔记3.3.3 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

• • 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 make the total vertical force on the object zero

Step 3. Calculate F_MAX= μR and find the resultant (total force) of all the horizontal forces on the object

• • 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

Step 4. Use F = ma to determine the acceleration of the object

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