Coefficient of Friction: Exceeding the Limits?

[gandharva_23]

Homework Statement

Can coefficient of friction between any 2 surfaces be greater than 1 ? If not why ?

 

[berkeman]

What do you think? Do you know how to do the simple experiment of tilting up a board to an angle theta until an object on the board starts to slide? What do you think would happen if both the board and the object were coated with sandpaper?

 

[gandharva_23]

if both the board and the object are coated with a sand paper then the object would slide when the board makes greater angle with the forizontal . how can i define coefficient of friction between 2 surfaces ?

 

[berkeman]

if both the board and the object are coated with a sand paper then the object would slide when the board makes greater angle with the forizontal . how can i define coefficient of friction between 2 surfaces ?

Not exactly what I was looking for. Draw a free body diagram of an object sitting on the board as the board is tilted up to some angle theta. Write the equation for the force summation along a line that is parallel to the board. At some theta as you tilt the board op, the object will break loose and start sliding down the board. That point is where the static coefficient of friction no longer supplies enough force back up the board (parallel to the board) in order to keep the object from slipping.

There is a surprisingly simple way to relate this critical angle theta to the static coefficient of friction $$\mu_S$$ Can you derive it, or have you seen it in your textbook?

Once you understand this relationship, and picture a high-mu setup like the board and object are both coated with sandpaper (as opposed to something slippery), then you should be able to answer your original question about whether mu can be over 1.

 

[gandharva_23]

There is a surprisingly simple way to relate this critical angle theta to the static coefficient of friction LaTeX graphic is being generated. Reload this page in a moment. Can you derive it, or have you seen it in your textbook?

you mean tan (theta) = mu relation ? ok i think i got it ... theta can be between 45 to 90 for high mu surfaces . that implies mu will be greater than 1 . am i right now ? How can i define coefficient of friction between 2 surfaces ?

 

[berkeman]

you mean tan (theta) = mu relation ? ok i think i got it ... theta can be between 45 to 90 for high mu surfaces . that implies mu will be greater than 1 . am i right now ?

Yes, that is exactly right.

How can i define coefficient of friction between 2 surfaces ?

I'm not sure what you mean by that. The coefficient of friction is always associated with a pair of surfaces, since it wouldn't make sense for a single surface to have a mu value alone. You can "define" the mu for a pair of surfaces just as you have done, with the mu = tan(theta) expression.

 

[gandharva_23]

thank you ......