Static friction describes the friction force
opposing the direction of motion when the
sliding velocity is zero, static friction is
defined as:
F = μR
Where,
F = Friction force
μ = Coefficient of Friction (COF)
R = |W| = Reaction force due to the
applied load W
Note the applied load is assumed to be
given by the mass above the contact area only (active area, coloured green in the diagram).
FRICTION FOR TWO
Using the initial example of two sheets of paper, by applying the above formula to some
convenient values we can calculate the friction force necessary to separate two sheets of
paper.
μ = 1 (reasonable assumption for paper-paper COF)
R = |W| = 2grams * 9.81m/s2 = 0.002 kg * 9.81m/s2 = 0.01962N
F = 1 * 0.01962N = 0.01962N
Two sheets of paper can be separated easily.
SCALING UP
Let us assume that each telephone book has 500 sheets and weighs 1kg. As the pages are
stacked upon one another, the average normal force is used to calculate the total friction force.
The number of friction contact surfaces – sheet surfaces or pages – defined as N, is directly
proportional to the friction force, giving,
F = NμRav
Inputting the values, we get,
μ = 1
Rav = |Wav| = 0.5 * (1 + 1)kg * 9.81m/s2 = 9.81N
N = Number of Contact Surfaces = Number of Sheets - 1 = (500 + 500) – 1 = 999
F = 999 * 1 * 9.81N = 9800.2N
From the above calculation, the friction force required to separate two phone books is
approximately one tonne-force (9.81kN). Not inseparable, but not far from it.
CASE CLOSED/IS THAT ‘NORMAL’?
Interestingly, using only two sheets but with the same contact area as all the sheets in the
phone book would give a friction force of F = 1 * 1 * 9.81N = 9.8N, 1000 times smaller.
Increasing the contact area between two sheets decreases the pressure (reaction force/area).
Increasing the contact area of stacked sheets (by adding sheets) does not decrease the
pressure (reaction force/area). When stacking, this creates a positive, direct relationship
between contact area and Coefficient of Friction. More sheets = higher COD = higher F.