A water wheel with radius Rw = 1.1 m and mass Mw = 1.05 x 103 kg is used to powe

Question

A water wheel with radius Rw = 1.1 m and mass Mw = 1.05 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. (a)Calculate the angular velocity w of the water wheel in radians/sec. (b)Calculate the kinetic energy Kw, in J, of the water wheel as it rotates. (c)Assume that 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. Randomized Variables: Rw = 1.1 m Mw = 1.05 x 103 kg fr = 2.1 Hz

Explanation / Answer

Rw = radius of wheel = 1.1 m

Mw = mass = 1.05*103 kg

fr = frequency = 2.1 Hz

a) Ww = angular velocity = ?

Ww = 2*pi*fr

= 2*3.14*2.1 =13.18 rad/s

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b) K.E = kinetic energy = ?

K,E = (1/2)*Iw*Ww2

Iw = moment of interia = Mw*Rw2 = 1.05*103*1.12 = 1270.5 kg-m2

K.E = (1/2)*1270.5*13.182 = 110.35*103 J

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C) P(power) = energy transferred / time

time = 1 sec

P = (20/100) *110.35*103 / 1 = 22070 W

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