HELPPP!!!!!! HAVE AN EXAM ON THIS AN I DONT UNDERSTAND!! A potter’s wheel is rot
ID: 1449126 • Letter: H
Question
HELPPP!!!!!! HAVE AN EXAM ON THIS AN I DONT UNDERSTAND!! A potter’s wheel is rotating around a vertical axis through its center at a frequency of 2.0 rev/s. The wheel can be considered a uniform disk of mass 4.8 kg and diameter 0.36 m. The potter then throws a 3.1 kg chunk of clay, approximately shaped as a flat disk of radius 11 cm, onto the center of the rotating wheel. (a)What is the frequency of the wheel after the clay sticks to it? (b) What fraction of the original mechanical energy of the wheel is lost to friction after the collision with the clay? I know a= 10rad/s ans b= 23%, I just don't know where he got this answer!
Explanation / Answer
(a)
i = 2.0 rev/s = 2.0*2* = 12.56 rad/s
Moment of Inertia of disk = 1/2*M*R^2
I1 = 1/2*4.8*(0.36/2)^2 = 0.077 Kg m^2
Moment of Inertia of Clay disk = 1/2*M*R^2
I2 = 1/2*3.1*(0.11)^2 = 0.0188 Kg m^2
Using Angular Momentum Conservation,
Initial Angular Momentum = Final Angular Momentum
I1*i = (I1 + I2)*f
0.077 * 12.56 = (0.077+0.0188)*f
f = 10.0 rad/s
Frequency of the wheel after clay sticks, f = 10.0 rad/s
(b)
Initial K.E = 1/2*I1*i^2
Final K.E = 1/2*(I1 + I2)*f^2
Energy Lost, = Initial K.E - Final K.E
Energy Lost, = 1/2*I1*i^2 - 1/2*(I1 + I2)*f^2
Energy Lost, = 1/2*0.077 * 12.56^2 - 1/2*(0.077+0.0188)*10^2
Energy Lost, = 1.28 J
Fraction of Energy Lost, = Energy Lost/ Initial * 100%
Fraction of Energy Lost, = 1.28/6.07 * 100%
Fraction of Energy Lost, = 21%
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