International A LevelMaths: Mechanics 1EdexcelRevision Notes3. Forces & Newton’s Laws3.3 Further Forces & Newton's Laws3.3.5 Coefficient of Friction - Harder Problems

Coefficient of Friction - Harder Problems (Edexcel International A Level Maths: Mechanics 1)

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Coefficient of Friction - Equilibrium

How is friction used when a body is in equilibrium?

  • When a body is in static equilibrium under the action of a number of forces, including friction, the value of friction will be less than or equal to the value of μR
  • When the value of friction is equal to μR, the body is in limiting equilibrium and is on the point of moving
  • When a body is stationary on an inclined plane then it is either in equilibrium or in limiting equilibrium, we cannot assume that F = μR

How is friction used when a body is moving?

  • When a body is moving under the action of a number of forces, including friction, the value of friction will be equal to the value of μR

Worked example

3.3.5_WE_CF Harder_1

A wooden block of mass m is stationary on a plane inclined at 25° above the horizontal. The coefficient of friction between the block and the plane is µ.  Find the least possible value of µ .

0n1-c-XM_3-3-5-coeff-of-frict-harder-problems-part-1-worked-solution

Examiner Tip

  • Always draw a force diagram and label it clearly.
  • Look out for key vocabulary such as rough, smooth, equilibrium, on the point of moving and limiting equilibrium and know how to use each.

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Coefficient of Friction – Connected Particles

How is friction used for connected particles?

  • When two particles are connected by means of a light, inextensible string, friction will act only on any particle that is resting on a rough surface
  • On an inclined slope, friction will act in the direction opposite to the direction the particle is moving in or on the point of moving in
  • The direction they will move in depends on both the weight of the particles and the angles of the slopes they are resting on
    • Compare the components of the weight in the direction of the motion the particles will move in
    • The particle with the heavier component will move down the slope

Worked example

3-3-5-worked-example-part-2-question

3-3-5-coeff-of-frict-harder-problems-part-2-worked-solution

3-3-5-coeff-of-frict-harder-problems-part-2-worked-solution-1

Examiner Tip

  • Be careful not to assume that the system will move in the direction of the heavier particle, remember to consider the angle too. Make sure your diagram is clear enough to work with, sometimes there can be a lot of information on the diagram.

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    Amber gained a first class degree in Mathematics & Meteorology from the University of Reading before training to become a teacher. She is passionate about teaching, having spent 8 years teaching GCSE and A Level Mathematics both in the UK and internationally. Amber loves creating bright and informative resources to help students reach their potential.