CIE A Level Maths: Mechanics復習筆記3.3.3 Coefficient of Friction - F = ma
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
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- 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?FMAX=?μR?and find the?resultant?(total force) of all the horizontal forces on the object
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- Remember – if the resultant of the other horizontal 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
- For non-horizontal surfaces see the notes on?inclined planes
Worked Example
Exam Tip
- 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.
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