A water wheel with radius R w =1.6 m and mass M w =1.8 X 10 3 kg is used to powe
ID: 1449845 • Letter: A
Question
A water wheel with radius Rw=1.6 m and mass Mw=1.8 X 103 kg is used to power a grain mill next to a river. Treat the water wheel as a hollow cylinder. The rushing water of the river rotates the wheel with a constant frequency fr=2.1 Hz.
(Part A) Calculate the angular velocity ww of the water wheel in radians/sec.
(Part B) Calculate the kinetic energy Kw, in J, of the water wheel as it rotates.
(Part C) Assume the every second, 20% of the kinetic energy of the water wheel is transmitted to the grain mill. Calculate the power Pw in W of the grain mill based on the energy it receives from the water wheel.
Explanation / Answer
given
R = 1.6 m
M = 1.8*10^3 kg
f = 2.1 hz
A) w = 2*pi*f
= 2*pi*2.1
= 13.2 rad/s
B) moment of inertia of the wheel, I = M*R^2
= 1.8*10^3*1.6^2
= 4608 kg.m^2
KE = 0.5*I*w^2
= 0.5*13.2*4608^2
= 1.4*10^8 J
c) Power output to the grain mill = 20% of 1.4*10^8 J/s
= 2.8*10^7 Watts
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