Hey all... Please show your work for these. Thanks ! Finding the Cartesian compo
ID: 2270011 • Letter: H
Question
Hey all... Please show your work for these. Thanks !
Finding the Cartesian components of a force described by direction angles Find the Cartesian components of force P acting in then x, y, and z directions given P = 50.0 N, alpha = 116.0 degree, beta= 89.0 degree, and gamma = 26.0 degree Recall that is the angle between the vector and the x axis. is the angle between the vector and the y axis, and is the angle between the vector and the z axis. Express your answers, separated by commas, to the nearest tenth of a newton. Find the angle between forces find the angle between F and P Express your answer to three significant figures in degrees. Determine the force along a member Determine the magnitude, FDA, acting along member DA,due to the applied force F = 7.60 I - 11.0 j +22.2 K N. Express your answer to three significant figures and include the appropriate units. Finding the component of a force perpendicular to a direction Given F = 7.60 i - 11.0 j + 22.2 kN find the component of F that acts perpendicular to member DA such that the vector addition of the perpendicular and parallel components of F (F = ) with respect to DA equals F. Express your answer in component form. Express your answers, separated by commas, to three significant figures.Explanation / Answer
A)
Px = P*cos alpha = 50*cos116 = -21.9 N
Py = P*cos beta = 50*cos89 = 0.9 N
Pz = P*cos gamma = 50*cos26 = 44.9 N
B)
F.P = (7.6 i - 11 j + 22.2 k). (-21.9 i + 0.9 j + 44.9 k) = (-7.6*21.9 - 11*0.9 + 22.2*44.9) = 820.44
|F| = sqrt (7.6^2 + 11^2 + 22.2^2) = 25.9 N
|P| = sqrt (21.9^2 + 0.9^2 + 44.9^2) = 49.96 N
theta = acos [(F.P) / (|F|*|P|)]
= acos [820.44 / (25.9*49.96)]
= 50.654 deg
C)
Vector DA = (-5.1 - 0)i + (4.38 - 3.47) j + (5.35 - 3.50) k
= -5.1 i + 0.91 j + 1.85 k
Magnitude of DA = sqrt (5.1^2 + 0.91^2 + 1.85^2) = 5.5
Unit vector in DA = (-5.1 i + 0.91 j + 1.85 k) / 5.5
= -0.927 i + 0.165 j + 0.336 k
Magnitude of component of F along DA = (7.6 i - 11 j + 22.2 k) . (-0.927 i + 0.165 j + 0.336 k)
= abs[(-7.6*0.927) - 11*0.165 + 22.2*0.336]
= 1.401 N
D)
F_parallel = 1.401*(-0.927 i + 0.165 j + 0.336 k)
= -1.299 i + 0.231 j + 0.471 k
F_perp = F - F_paralel
= (7.6 i - 11 j + 22.2 k) - ( -1.299 i + 0.231 j + 0.471 k)
= 8.899 i - 11.231 j + 21.729 k