Speed Turnable
September 16th, 2007
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Speed Turnable
college physics 1 college physics 1?
a coin is placed 11.0 cm from the axis of a rotating turnable of variable speed. when the speed of the turnable is slowly increased, the coin remains fixed on the turnable until a rate of 36 rpm is reached and the coin slides off. what is the coefficient of static friction between the coin and the turnable?
The force on the coin from the rotation of the turntable increases with the speed of the turntable. The frictive force between coin and truntable to resist this motion increases with that force, but cannot go above a maximum level, determined by the coeffecient of friction, in this formula:
F = µR
where F is friction, R is reaction of turntable to weight of coin, and µ is coefficient of friction.
The force pushing the coin outwards is the centripetal force
F = mv² / r
where r is distance from coin to centre of turntable, m is its mass and v is its velocity.
The coin starts to slip when the maximum friciton is equal to the centripetal force, so when
mv² / r = µR
since reaction R=mg, this becomes
mv² / r = µ mg
v² / r = µg
=>
µ = v² / rg
We know velocity v as distance travelled divided by time, since at 36rpm the coin travels 36 circumferences every 60 seconds, that is v = 36* 2π * 11cm every 60 seconds =>
µ = (36 * 2π * 11cm / 60seconds)² / rg
we know r=11cm and g=9.81m/s²
so
µ = (36 * 2π * 11cm / 60seconds)² / (11cm * 9.81 m/s²)
Convert cm into m =>
µ = (36 * 2π * 0.11 / 60)² / (0.11 * 9.81)
µ = 0.16
Voila!
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