Homework 2

Introduction to Machinery Principles

You can use this document to insert your answers or submit handwritten documents. Only hardcopies will be accepted, no emails. The score for late HWs will be reduced by 20% if submitted by the beginning of the next class day after the due date. After that, the score will be zero.

The HWs can be typed or handwritten, but for maximum credit, they must be neatly written, organized, and complete. Write down important formulas that you are using. Show your calculations and carry at least five significant digits in your calculations, and record four s.d. in your answers.

Read Ch01 in Chapman.
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1.     (4 pts) A flywheel with a moment of inertia of C kg×m2 is initially at rest. If a torque of D N×m (counterclockwise) is suddenly applied to the flywheel, what will be the speed of the flywheel after 5 seconds? Express the speed in both radians per second and revolutions per minute.

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2.     (2pts)What is the mathematical relationship between the magnetic field intensity vector and the magnetic flux density vector? What are the units for each?

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3.     (6 pts)Using the following figure:

a) Write the integral form of Ampere’s Law in terms of the magnetic field intensity H.

b) Calculate the magnitude of H in the core.

c) If the relative permeability of the core is DEFA, calculate the magnitude of the magnetic flux density induced in the core.

d) Calculate the magnetic flux  through the area Ac.

e) Calculate the magnetomotive force generated by the coil

f) Calculate the reluctance of the core circuit.

i  = G  amps

lc  = B meters

Ac = 0.0G  meters2

N  = DFA


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4.     (1 pt) What is the mathematical relation between the reluctance of a material with respect to the permeability, mean length of the loop, and cross sectional area of core?

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5.     (3 pts) A ferromagnetic core is shown in the figure below. The depth of the core is 5 cm. The other dimensions of the core are as shown in the figure. Assume that the mean path length of the flux is in the center of each of the four legs of the core (red lines), and ignore the spreading at the corners of the core. For the relative permeability, use .

a) Calculate the total reluctance of the core by calculating the total reluctance of each leg.

b) If the magnetic flux  is 0.00BWb, calculate the magnetomotive force and the current in the core.

c) With this current, what is the flux density at the top of the core? What is the flux density at the right side of the core?

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6.     (2 pts) Give a brief answer to the following:

a) What is a magnetic domain in a ferromagnetic core material?

b) If an external magnetic field is applied to the core, what effect does this have on the magnetic field in the core?

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7.     (1 pt) What is the voltage induced across a coil which has GF turns and the rate of change of flux in all of them is B Wb/s ?

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8.     (3 pts) Calculate the effective (or RMS) value of the waveform in the figure below and the average power delivered to a B Ω resistor when the effective voltage is applied across the resistor.



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9.     (3 pts) For the power system in the figure below, find:

a) the average power,
b) the reactive power,
c) the power factor.

Note that the supply voltage ABC  V is an RMS value. (Hint: Find the complex power consumed by each impedance using the voltage.)


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10. (2pts)A wire carrying a current 0.B amperes with length A meters in the presence of magnetic flux density 0.DC tesla is shown in the figure below. What are the magnitude and direction of the force induced on the wire?

11.

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12. (2pts)A moving conductor with a velocity of A0 meters/sec to the right in a magnetic field with flux density 0.E tesla is shown in the figure below. The flux is out of the page, and the length of the conductor in the field is C meters at an angle of B0° with the vertical. What is the resulting magnitude of the induced voltage and its polarity?

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13. (2 pts) Calculate the power factor for the following circuit.



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14. (3 pts) An AC voltage source V is supplying power to a load with impedance Z as shown in the figure below. Calculate the current I supplied to the load, the power factor of the load, the real, reactive, apparent, and complex power supplied to the load.

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