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A student builds a simple axial flow-ventilating fan driven by a motor to provide some relief during summer. The motor delivers 0.4 kW of power to the fan blades. She observes the fan produces an outlet stream of air with a diameter of 0.6 m having a speed of 12 m/s. Assume that the flow upstream of the fan has negligible speed. Assume density of air to be 1.23 kg/m3 and room temperature to be 20o C. Assume all losses are due to friction (heat).
[a] Determine how much power from the motor produces useful effects (for the student).
[b] Estimate the mechanical efficiency of this fan.
A sphere of radius R is uniformly charged to a total charge of Q. It is made to spin about an axis that passes through its center with an angular speed ω. Find the magnitude of the resulting magnetic field at the center of the sphere.
A resistor is in the shape of a cube, with each side of resistance R . Find the equivalent resistance between any two of its adjacent corners.
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