Questions 1. Use the component method and determine the resultant of the followi
ID: 1581378 • Letter: Q
Question
Questions 1. Use the component method and determine the resultant of the following three vectors: () 100, at 30° (B) S0, at 45% and (C) 150, at 90° What is the magnitude and the angle for the equilibrant vector? 2. If the masses of the hangers are equal, can their weight be neglected? Explain. 3. Can two vectors of equal magnitude add up to give the zero resultant vector? A particle executes three consecutive displacements of 3 meters, 4 meter, and 5 meters and returns to the initial position. How are these displacements oriented? 4.Explanation / Answer
Answer 1:
To determine the resultant of vectors by component method, we need to add the individual components of individual vectors. As this is a two-dimensional system, we need to add only two components, i.e. x-component and y-component.
For that, first we need to resolve all threee vectors into their x and y components and then add their components seperately to get the components of the resultant vector.
X-component of the first vector = 100 x cos(30) = 100 x 0.866 = 86.6
Y-component of the first vector = 100 x sin(30) = 100 x 0.5 = 50
X-component of the second vector = 50 x cos(45) = 50 x 0.707 = 35.4
Y-component of the second vector = 50 x sin(45) = 50 x 0.707 = 35.4
X-component of the third vector = 150 x cos(90) = 150 x 0 = 0
Y-component of the third vector = 150 x sin(90) = 150 x 1 = 150
X-component of the resultant = X-component of first vector + X-component of second vector + X-component of third vector = 86.6 + 35.4 + 0 = 122
Y-component of the resultant = Y-component of first vector + Y-component of second vector + Y-component of third vector = 50 + 35.4 + 150 = 235.4
So, the resultant vector is:
R=122 i +235.4 j (where i and j represent unit vectors in x and y directions respectively).
Magnitude of equilibrant is same as magnitude of the resultant, i.e.
((122)2+(235.4)2) = 265.1
Angle of equilibrant is negative of the angle of resultant:
-tan-1(y/x) = -tan-1(235.4/122) = -62.6o
(as the resultant and equilibrant form pair of equal and opposite vectors)
Answer 2:
It depends on what is the application or problem at hand. Some problems that consider hangers as point masses, their weight can be neglected, but for problems that require moment about an axis, the weight cannot be neglected.
Answer 3:
Yes, two vectors of equal magnitude can add up to zero resultant vector, if they are in opposite directions. For example, a resultant vector and an equilibrant vector add up to zero and bring the body in equilibrium.
Answer 4:
The three displacements form the three sides of a right-angled triangle, the displacement 3m is along the positive x-direction, the displacement 4m is along the positive y-direction, and the displacement of 5m is downwards along the hypotenuse, bringing it back to the starting point.
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