Rotational Motion, Magnetic Fields, and complex Numbers - Engineering Assignment Help

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ASSIGMENT 2

Rotational Motion, Magnetic fields, and complex Numbers11540067000ASSIGMENT 2 Rotational Motion, Magnetic fields, and complex Numberscenterbottom[Nombre de la compañía] | [Dirección de la compañía]1154000[Nombre de la compañía] | [Dirección de la compañía]center790008446770Design of a wind turbine
antonio de la rosa
1154000Design of a wind turbine
antonio de la rosa
right23002457452021
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ASSIGMENT 2
Index:
Task 2.1 Rotational motionTask 2.2 Magnetic fieldsTask 2.3 Complex numbersTask 2.1 Rotational motion 2.1.1 A motor’s shaft is spinning at a speed of 1800 rpm. What is the shaft speed in radians per second?
Answer: 1800 rpm*radsec*1min60sec*2?1rev=60?radsec2.1.2 A flywheel with a moment of inertia of 4 kg?m2 is initially at rest. If a torque of 6 N?m is suddenly applied to the flywheel, what will be the speed of the flywheel after 5 s? Express that speed in both radians per second and revolutions per minute.
Answer: 1800 rpm*5sec=7.5radsec;7.5radsec*60sec1min*1rev2?=71.92 rpm2.1.3 The motor in task 2.1.1 develops a (net) mechanical torque on the shaft of 9.55 Nm. Calculate the (net) mechanical power output (net shaft power) of the motor.
Answer: 60?radsec*9.55Nm=1.80kW2.1.4 The electric input power to the motor in task 2.1.3 is measured at 2.0 kW. Calculate the efficiency of the motor for the specified operating conditionAnswer: 1.80kw2kw=0.9Task 2.2 Magnetic fields2.2.1 Induced voltage (emf) in a coil. A flat square coil has 10 turns. Each of the sides are 25 cm long. A magnetic field of 0.4 T is passing through the coil, perpendicular to the plane of the coil. See figure 1.
a) If nothing is changed in figure 1, what is the induced emf?
Answer: 0 as there is neither movement or a variation of intensity, ther for emf will not chnnageb) The magnetic field is increased from 0.4 T to 0.8 T in 5 seconds at a steady rate. While the change is taking place, what is the induced emf in the coil?
?=(0.4+0.45t)*0.252?=-N*d?dt=-10*0.45*0.252=-0.05Answer:-0.05 V
c) While the magnetic field is changing, the induced emf causes a current to flow in the coil. Which direction will this current flow? Clockwise or counter-clockwise?
Answer: Clockwise; By creating an opposite forcé to the magnetic field and using the right¨s hand rule we conclude the directión of the current Flow Will be clockwise.
2.2.2 Induced voltage on a conductor moving in a magnetic field (emf). A wire is shown in figure 2 that is moving in the presence of a magnetic field. With the information given in the figure, determine the magnitude and direction of the induced voltage in the wire.
?=V*B*l=V*B*L*cos?=10*0.2*0.25*cos45=10*0.05*22=-24Answer: -2/4

2.2.3 Loop rotating in a uniform magnetic field. The simple loop rotating in a uniform magnetic field shown in figure 3 has the following characteristics:
a) Calculate the voltage etot(t) induced in this rotating loop.
?=?AB+?CB+?CD+?DA=2*l*V*B*sin?=2*B*l*r*w*sinwt=22.6*sin?(377)Answer:22.62*sin(377)
b) What is the frequency of the voltage produced in this loop?
Answer: f=w/2 ? = 60Hz
c) Suppose that a 10 ? resistor is connected as a load across the terminals of the loop. Calculate the current that would flow through the resistor.
I=?R=B*L*R*W*sin?(wt)10=2.262*(377t)Answer: 2.262*(377t) d) Calculate the instantaneous and average electric power being generated by the loop for the conditions in (c).
Pinstant=22.62*sin377t*2.26*sin377t*dt=51.12*sin2377*t*dtPaverage=1TPinstnat=3607*sin2377t*dtTask 2.3 Complex numbersGiven the following complex numbers:
2.3.1 Multiplication Calculate ???????? ? ???????? and give the result in both rectangular form and polar form. (Show your calculation procedure).
320802027178023.087<4.97 (POLAR FORM)
400002000023.087<4.97 (POLAR FORM)
Answer: (2+3i)*(4-5i) = 8-10i+12i-(-15) =23+2i (COMPLEX FORM)
2.3.2 Division Calculate ????????/???????? and give the result in both rectangular form and polar form. (Show your calculation procedure).
Z1Z2=2+3i4-5i*4+5i4+5i=-7+22i41=-0.17+0.54i
Module=0.57
Angle= arct(0.54-0.17)=-72.52Z1/Z2=0.57<-72.52º
2.3.3 Calculate the product ????1 ? ????2and give the result in both rectangular form and polar form (Show your calculation procedure)
Module= 6.5*2.5=16.25
Angle=64-33=31
Z1*Z2=16.25<31º
Z1*z2=16.25*(cos31+i*sin(31)=13.93+8.37i
2.3.4 Calculate the quotient ????1/????2 give the result in both rectangular form and polar form (Show your calculation procedure)
Z1Z2=2.6*(cos-97+sin-97i=-0.32-2.58i (COMPLEX FORM)
Z1Z2=2.6<97º (POLAR FORM)

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