Name: Joe H.
What does the "u" symbol mean in the formula of
This is for a science lab in 8th grade with a problem that asks: If a
brick is sliding along a bench, how does the frictional force depend on
the weight of the brick?
If you could give me any info on these topics that would be great.
u is the coefficient of sliding friction, an index so to speak that is
less than 1.0.
For your problem, F is the friction force on the brick and R is the
weight of the brick. The greater the weight of the brick R increases and
F (the frictional force retarding the motion of the object also
increases). The increase of R and F is about the same, u is usually
independent of the weight and depends on the surface which the block is
moving and the surface which the block is moving on. Smooth surfaces
have lower friction coefficients, rough surfaces have higher
The frictional force depends on the force pushing two things together
and on the surfaces of the two objects. If "R", in your equation stands
for the force pushing the things together, then "u" stands for the
coefficient of friction, which tells you something about the two
surfaces, but which really is just a convenient name for the ratio F/R.
If the surfaces are coated with something very rough or sticky, then the
frictional force is going to be huge even if you don't press the surfaces
together very hard, so the coefficient u=F/R is going to be large. If
the surfaces are really slippery, the you won't get much frictional force
even if you mash the surfaces together as hard as you can, so u=F/R is
going to be small.
If a brick is sliding along a bench, and the bench is horizontal, then the
full weight of the brick is the "R" of F=uR, and the frictional force is
just proportional to the weight. If the bench is tilted at an angle Q
from the horizontal, then only part of the weight of the brick (W cos(Q))
is acting to mash the surfaces together, and the rest (W sin(Q)) is just
pulling it along the bench. In this case, you'd have to say F=uR=uWcos(Q).
The 'u' is the greek letter mu. It stands for the coefficient of friction.
It is found by dividing the force due to friction divided by the support
force. If you divide the force by which you are pulling or pushing the
object at hand by the force acting at a 90 degree angle by the surface the
object is sliding on (called the support force), you get a unitless
quotient. This quotient, represented by the letter mu, is the coefficient
There is no known way of looking at two materials and then calculating the
coefficient. For any particular set of materials, the coefficient must be
measured. Many of the coefficients of friction for a wide assortment of
materials are listed in the Handbook of Chemistry and Physics.
---Nathan A. Unterman
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Update: June 2012