A19.0-g metal cylinder is placed on a turntable, with its center76cm from the tu
ID: 2094555 • Letter: A
Question
A19.0-g metal cylinder is placed on a turntable, with its center76cm from the turntable's center. The coefficient of static friction between the cylinder and the turntable's surface is?s=0.89.A thin, massless string of length 76 cm connects the center of the turntable to the cylinder, andinitially, the string has zero tension in it. Starting from rest, the turntable very slowly attains higher and higher angular velocities, but the turntable and the cylinder can be considered to have uniform circular motion at any instant. Calculate the tension in the string when the angular velocity of the turntable is70rpm (rotations per minute).
Explanation / Answer
frequency = 70/60 Hz
? = 2pif = 2pi/70/60 = 140pi/60 rad/s
the centrifugal force is
Fc = m?^2*R
Fc = 0.019*(140pi/60)^2*0.76 N
the friction force is
Ff = mg?
Ff = 0.019*9.81*0.89
The tension is
T = Fc - Ff
T = 0.019*(140pi/60)^2*0.76 - 0.019*9.81*0.89
T = 0.604 N