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Name: Joe H.
Status: student
Age: 14
Location: N/A
Country: N/A
Date: 1999 


Question:
What does the "u" symbol mean in the formula of friction: F="u"R? 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.


Replies:
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 coefficients.

H. Myron


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).

Tim Mooney


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 of friction.

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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