Vectors and Static Equilibrium I. Algebraic Approach a. Compute the sum of force
ID: 3279142 • Letter: V
Question
Vectors and Static Equilibrium I. Algebraic Approach a. Compute the sum of force vectors A and B (determine b. Determine the magnitude and direction of the third c. Compute the sum of force vectors A, B, and C d. Determine the magnitude and direction of the fourth magnitude and direction) vector that will satisfy the equilibrium condition (determine magnitude and direction) vector that will satisfy the equilibrium condition II. Graphical Approach a. Add force vectors A and B using the tip tail method b. Measure the magnitude and direction of the resultant vector. c. Add force vectors A, B and C using the tip - tail method d. Measure the magnitude and direction of the resultant vector III. Comparison of results a. Compute the percent error for both magnitude and direction between the algebraic approach (accepted values) and the graphical approach (experimental values) A= 50 grams at 45. B = 100 grams at 135 C = 50 grams at 215.Explanation / Answer
1
a Compute A + B
Ax = 50 cos 45
Ay = 50 sin 45
Bx = 100 cos 135
by = 100 sin 135
A + B = (50 cos 45 + 100 cos 135 ) X + ( 100 sin35 + 50 sin 35) Y
=-35.3 x + 86.03 y
| A+ B| = 93
direction = 112.2 degrees.
b Magitude of 3rd vector = -35.3 x - 86.03y . As it is reverse of resultant
c. A + B + C
Cx = 50 cos 215 = -40.95
Cy = 50 sin 215 = -28.6
A + B + C = -35.3 x + 86.03 y + ( -40.95 x - 28.6 y)
= -76.25x + 57.43y
| A + B + C | = 95.48
direction = 143 degrees
d) 4th vector = - ( resultant)
= 76.25 x - 57.43 y
2. On graphical methrod
1) A + B = 92.8
2) A+ B +C = 95.2 cm
3. Here percentage error = 0.2 % error
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