Question

A water wheel with radius Rw = 1.2 m and mass Mw = 1.9 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 = 2.6 Hz.A. Calculate the angular velocity ωw 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.

Answer 1

Answer:

A. $w=16.33 rad/s$

B. $E_k=182401.576 J$

C. $P_w=36.48kW$

Explanation:

A.

Given

$R_w=1.2m$, $m_w=1.9x10^3 kg$, $f=2.6Hz$

The angular velocity is:

$w=2*\pi *f$

$w=2*\pi *2.6Hz$

$w=16.33 rad/s$

B.

Kinetic energy

$E_K=\frac{1}{2}*I*w^2$

$I=\frac{1}{2}*m*r^2=\frac{1}{2}*1.9x10^3kg*(1.2m)^2$

$I=1368.0(kg*m^2)$

$E_k=\frac{1}{2}*1368 (kg*m^2)* (16.33 rad/s)^2$

$E_k=182401.576 J$

C.

kinetic energy every second so:

$P_w=0.2*182401.5276J=36480.3 W$

$P_w=36.48kW$