Hint 1. Replace the /ItalicAngle 0 Grading Policy. (b) Fh = 300lb and Fv = -200lb . So we can say that a phasor represent a scaled voltage or current value of a rotating vector which is frozen at some point in time, (t) and in our example above, this is at an angle of 30o. (b) Determine the, single force that is equivalent to the force-couple system obtained in parl a, and specify its point of application the level, SOLUTION First note 'hat the two 90-N forces form a couple. Other uncategorized cookies are those that are being analyzed and have not been classified into a category as yet. The length of the line segment represents the magnitude of the vector, and the arrowhead pointing in a specific direction represents the direction of the vector. A: Let's consider the force 260 lb is making an angle ? (PDF) ENGN.2050-202 Assignment 10 Solution - Academia.edu /FontName /Times#20New#20Roman /Type /Page Each position along the horizontal axis indicates the time that has elapsed since zero time, t=0. As phasor diagrams can be drawn to represent any instant of time and therefore any angle, the reference phasor of an alternating quantity is always drawn along the positive x-axis direction. Given vector $v_1 = (8, -4)$, calculate the the magnitude. The vector P = 3i-j+k. endobj %%EOF The order does not matter; either one can be calculated first. Assume You'll get a detailed solution from a subject matter expert that helps you learn core concepts. Select the correct the equation of equilibrium for the pulley in the y direction in terms of the tension in rod BD, , the tension in the A) Is any combination of forces that is equivalent to the original system of forces. endobj But opting out of some of these cookies may affect your browsing experience. 3. A: The problem will be solved in two parts and has been mentioned below. direction of the 8- force. Explanation: The forces at B and C used to form a couple M is given by. This calculator performs all vector operations in two and three dimensional space. 778 611 778 722 556 667 722 722 0 0 722 0 0 0 0 0 0 0 500 556 444 556 444 Example 04: Find the dot product of the vectors $ \vec{v_1} = \left(\dfrac{1}{2}, \sqrt{3}, 5 \right) $ and $ \vec{v_2} = \left( 4, -\sqrt{3}, 10 \right) $. From the free-body diagram, Express each force in Cartesian vector form. Express each coordinate rounded to three significant figures, if necessary. Then a Phasor is a quantity that has both Magnitude and Direction. /Subtype /TrueType Representation of Vector - Examples, Magnitude, FAQs - Cuemath 556 722 611 0 0 0 556 0 0 0 0 0 0 500 500 444 500 444 278 500 500 278 278 Drawn to a scale of 1 cm =5 N, the vector representing F 1 will be 4 cm long and the vector representing F 2 will be 5 cm long. The forces at B and C used to form a couple M is given by. Find the moment of the couple acting on the rod - YouTube Express your answer to three significant figures and include the appropriate units. Voltage, V1 of 20 volts leads voltage, V2 by 60o, then it has both horizontal and vertical components as follows. In this tutorial we'll learn how to find: magnitude, dot product, angle between two vectors and cross product of two vectors. given force-couple system with an equivalent force-couple system at corner H. A Cartesian vector representation of the equivalent force at H is ( lb) i + ( The dot product must be calculated first. Or, do I need to put everything in sinusoidal functions using positive frequency (it is easy to convert the negative frequency functions to positive frequency functions. y3 = 4.5 sin(t-450), Very fundamental and explain in simple language so it is easy for understanding. Add the couple C= 40i-30j +50KN.m to the resultant vector of the three couples 20N.m-30 N.m and 170 N.m acting in the xy,yz and xz planes respectively. Frames and machines: Example 05: Find the angle between vectors $ \vec{a} = ( 4, 3) $ and $ \vec{b} = (-2, 2) $. Forces in Cartesian Vector Form - Question Solutions 91 0 obj For this reason . hb```f`` Two 80-N forces are applied as shown the comers ard D of a rectangular Plata (a) Determine the moment of the coupe formed bythe fomes by resolving each fcnce into hmimnta_ and vertical com}nnents adding the moments of the two lesulting coupley (b) Use the lesult obtained to determine the erFendicuIar distance be tween lines BE and DF 1.The tension in cableDA has a magnitude of TDA lb. >> A) Fx = 0, Fy = 0, and Mo = 0. D) The summation of the forces in the x direction equals zero, the summation of the forces in the y direction equals zero, and the summation of the moments about any point on or off the body is zero. as a point particle in this problem). The 20- force acts in two directions (as described by the 3, 4, 5 0000001802 00000 n For example, we visualize the vector (4, 2) (4,2) (4, 2) left parenthesis, 4, comma, 2, right parenthesis as an arrow whose tail is at the origin and whose tip is at the point (4, 2) (4, 2) (4, 2) left parenthesis, 4, comma, 2, right parenthesis. /O 90 c%l[HdQ%Xm$ unknown external reactions. B) M = F r . Solution : (A) Determine the Magnitude of the equivalent couple and the direction of its axes Step 1: Determine Equivalent Couple & Couple Vector (Beer et al.,2009) The magnitude of couple along X axis - Mx = 3 lb ft The magnitude of couple along Y axis - My = 0 The magnitude of couple along Z axis. ,CPr)AIiLrjtYPi{FU7r%!b_Em*w-37W#TCEOo? The length of the line segment represents the magnitude of the vector, and the arrowhead pointing in a specific direction represents the direction of the vector. The cross product must be calculated first. /S 150 /Ascent 891 Use exact expressions for irrational numbers instead of rounding 0000000750 00000 n The order does not matter; either one can be calculated first. 97 0 obj Is the moment positive or negative? Two forces: one that acts vertically and one that acts horizontally /ID [] Functional cookies help to perform certain functionalities like sharing the content of the website on social media platforms, collect feedbacks, and other third-party features. C) Do not deflect under loads. What is the unit vector from A to B,? 3. equivalent force-couple system at G. A Cartesian vector representation of the equivalent force is ( kN) j. C) Support tension or compression and resist bending and shear but cannot resist torsion. Tension in cable BC For example, voltage and current. Hint 1. A vector that has an arrow head at one end which signifies partly the maximum value of the vector quantity (Vm or Im) and partly the end of the vector which rotates. opposite direction of the two 3- forces. new free-body diagram for the pulley and set up the equilibrium equations for both component directions. B) There was a mathematical error in the calculations. /Group << /Type /Group /CS /DeviceRGB /S /Transparency >> For a Star connected 4-wire supply, the voltage, (Vp) between any phase and neutral is measured as 240V in the UK and Europe, (now reduced to 230Vrms) and 120V in the USA. For a three-phase supply, the magnetic field on the rotor of the generator links in sequence with three equally spaced windings, or phases, on its stator producing an equally spaced three-phase supply. When writing the equations of equilibrium, recall that the weight acts only in the negative y direction: Hint 2. Problem-solving process b. However, as the current waveform is now crossing the horizontal zero axis line at this instant in time we can use the current phasor as our new reference and correctly say that the voltage phasor is leading the current phasor by angle, . /Flags 32 The dot product takes two vectors and returns a scalar given by ES 1021 - Assignment 2 Part B - Tutorial Assignment - Studocu The current phasor lags the voltage phasor by the angle, , as the two phasors rotate in an anticlockwise direction as stated earlier, therefore the angle, is also measured in the same anticlockwise direction. Given uAF=1.5/6.5i+2/6.5j6/6.5k, uAE=1/3i2/3j2/3k, uAG=2/7i+3/7j6/7k, and magnitude of the force FAF=1083 N. Find the projection on line AE of the force in cable AF. Quantities that have magnitude and direction but not position. Now that both the real and imaginary values have been found the magnitude of voltage, VT is determined by simply using Pythagorass Theorem for a 90o triangle as follows. 0000002638 00000 n A) M = r F . Please how is it calculated?? /Type /Font 500 500 500 500 500 278 278 0 564 0 0 921 722 667 667 722 611 556 722 722 A couple acts on a beam as shown below. reference point to use is one where multiple forces are applied. /Group << /Type /Group /CS /DeviceRGB /S /Transparency >> 4. Necessary cookies are absolutely essential for the website to function properly. Hint 2. 0000001530 00000 n xU]k0}5l}[P Calculate the magnitude and phase of the voltage V. A. Generally, when constructing a phasor diagram, angular velocity of a sine wave is always assumed to be: in rad/sec. The tension in rod BD is The cross product of vectors $ \vec{v} = (v_1,v_2,v_3) $ and $ \vec{w} = (w_1,w_2,w_3) $ is given by the formula: Note that the cross product requires both of the vectors to be in three dimensions. units. 0000002965 00000 n Moment couple = 2120 lb in Hint 2. the vectors will not be graded. This arises in induction generators and requires caution in circuit analysis for negative frequencies. 8KN, 5KN, 3KN /StemV 40 ANSWER: The image below shows a beam subject to two couples, and. A Cartesian vector representation of the equivalent couple is ( kNm) i + (
determine the vector representation of the couple shown
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