S2.8 Frictional force
[A] About the force
- The friction force FF is the interaction force between two surfaces in contact, acting parallel to the surfaces, inhibiting sliding.
- The value of FF depends both on the applied force parallel to
the surface, FA and the normal contact force between the surfaces, FN:
- no sliding:
FF=FA
- on the point of sliding:
FF=μsFN=FA
- while sliding:
FF=μkFN<FA
- no sliding:
- The quantities μs and μk are the coefficients of static and kinetic friction.
- They depend on the surfaces in contact; μk is smaller than μs.
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[B] Example problem
A block of mass m=2 kg rests on a plane inclined at an angle
θ=45∘ to the horizontal. A force ![]() |
Write down equations for (a) the normal contact force between box and plane and (b) the net force acting up the plane. Deduce the value of the coefficient of kinetic friction.

Solution
First things
- choose system: the mass
- identify forces: FG, FN and FF
- draw free body diagram
- choose coordinates
Apply 2nd law
Block moves at constant velocity; so net force on it must be zero.perpendicular to plane (y-direction):
0=may=FAsinθ+mgcosθ-FN
parallel to plane (x-direction):
0=max=FAcosθ-mgsinθ-FF
Invoke knowledge of forces
- During slipping: FF=μkFN
- Hence
Results
![\[ \mu_k = \frac{F_F}{F_N} = \frac{F_A\cos{\theta} -mg\sin \theta}{ F_A\sin{\theta} +mg\cos \theta} = \frac{30-20}{30+20} =0.2 \]](mastermathpng-2.png)
Check It!
- Are the units OK?
- Does it make sense?
Learning Resources
![]() | HRW Chapter 6.2-6.3 |
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