Deriving Coefficient of Static Friction for Inclined Textbook and Coin

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The discussion revolves around deriving the coefficient of static friction between a textbook inclined at an angle theta and a coin. The equation proposed is u = Ff(static)/Fnormal, with Ff determined as FgxSINxTheta and Fnormal as FgxCOSxTheta. Participants confirm that the gravitational force down the ramp is mg sin(theta) and the normal force is mg cos(theta). The final expression for the coefficient of friction is validated as μ = |-(mg) sin(theta)/(mg) cos(theta)|, which aligns with the initial equation provided. The conclusion is that the derived equation for the coefficient of static friction is correct.
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ok, our class got an assignment where we have to derive an equation for coefficient of static friction between our textbook (inclined at an angle theta) and a coin. The vale of the angle and the mass of the coin are not given. I have come up with the following equation and need to know if it is correct.

u = Ff(static)/Fnormal
*using components of the force of gravity, i determined Ff to be FgxSINxTheta and Fnormal to be FgxCOSxtheta
so,
u = FgxSINxTheta/FgxCOSxtheta

does this seem correct?

thanks for looking.
 
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mg sin\theta is the gravitational force down the ramp, so
-(mg) sin\theta is the force of static friction.

mg cos\theta is indeed the force normal

\mu=\frac{F_{friction}}{F_{normal}}

\mu must be positive, so
\mu=\mid \frac{-(mg) sin\theta}{(mg) cos\theta}\mid

Which looks exactly like what you got except you call it Fg and I called it mg
 
thanks, i just asked a friend and he got the same thing, so this must me right :smile:
 
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