Physics problem.. Show why µs = .16?
A coin is placed 11.0 cm (.11m) from the axis of a rotating turntable of variable speed. When the speed of the turntable is slowly increased, the coin remains fixed on the turntable until a rate of 36 rpm (which I approximated to be 2160 rps) is reached and the coin slides off. What is the coefficient of static friction between the coin and the turntable?
Please help.. I keep getting a different answer. I guess µs = 0.16. Please show work.
Please.. don't just give me the answer.. I have that! I need to know why µs = 0.16? Thank you!
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the motion occurs when the force due to rotation acting on the coin exceeds the frictional force, so we want to equate these forces to see when they are equal (as soon as the rotational force exceeds the frictional force, we get motion)
the rotational force comes from the centripetal force = mv^2/r
the frictional force = us mg
equate:
mv^2/r = us mg =>
us =v^2/(rg)
solve for v: v=dist/time = 36 x 2 pi r/60s
since one revolution = 2 pi r (the circumference of a circle); there are 36 revolutions per min, so the speed is 0.41m/s
substitute this into the equation for us:
us = (0.41m/s)^2/(0.11m x 9.8m/s/s)=0.16