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Pearson Edexcel IAL Mathematics M1.5.3 Coefficient of friction

Practise equilibrium with rough planes and surfaces, using limiting friction to find µ, force ranges, and whether a particle will stay at rest.

Syllabus
First assessment 2019
Course
Mathematics YMA01
Level
AS

Exam points

  • use F ≤ µR or F = µR at limiting equilibrium after resolving for the normal reaction
  • find minimum or maximum applied forces by choosing the correct friction direction
  • compare required friction with maximum friction to justify whether a particle remains at rest

M1.5.3 - Coefficient of friction question 1

[Maximum number: 4]
Figure 5

Figure 5

A parcel of mass 2 kg is pulled up a rough inclined plane by the action of a constant force.

The force has magnitude 18 N and acts at an angle of 40^ to the plane.
The line of action of the force lies in a vertical plane containing a line of greatest slope of the inclined plane.

The plane is inclined at an angle of 30^ to the horizontal, as shown in Figure 5.
The coefficient of friction between the plane and the parcel is 0.3
The parcel is modelled as a particle P

The points A and B lie on a line of greatest slope of the plane, where A B=5 m and B is above A. Particle P passes through A with speed 2 ms^-1 in the direction AB.

The force of 18 N is removed at the instant P passes through B. As a result, P comes to rest at the point C.

Determine whether P will remain at rest at C. You must show all stages of your working clearly.

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