6 Problems (3)
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Transcript of 6 Problems (3)
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Ch2 Main Ideas
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GROUP PROBLEM SOLVING I
1) Find the force vector F and unit vector uAB
2) Use Vector Dot Product to determine the projected component of F parallel and perpendicular to diagonal AB
Given: A 90 lb force is acting parallel and perpendicular to diagonal AB
Find: The magnitudes of the components of force
Plan:
xy
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GROUP PROBLEM SOLVING I (continued)
Solution:
F = 90(-cos60° sin45° i + cos60° cos45° j + sin 60° k)
F = (-31.82i +31.82j + 77.94k) lb
The magnitude of the projected component of F parallel to the diagonal AB is:
F perpendicular to the diagonal AB is:
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GROUP PROBLEM SOLVING II
1) Find F and uOA.
2) Determine FOA
Given: The Force F= 300 N
Find: Magnitude of the projected component of the Force along OA
Plan:
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Solution: Force and Unit Vector: The force vector F and unit vector u OA must be determinedfirst. From Fig. aF ={ (-300 sin30) sin 30 i + (300 cos30) j
+ 300 sin30 cos30 k} N ={-75 i + 259.81 j 129.9 k } N
GROUP PROBLEM SOLVING II (continued)
The magnitude of the projected component of F along line OA is:
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Ch3 Main Ideas
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Ch4 Main Ideas
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GROUP PROBLEM SOLVING V
1) Find r
2) Determine MO = r F
Given: F = {600i + 300j – 600k} N
Find: Determine the moment of the force about point A.
Plan:
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Solution:
GROUP PROBLEM SOLVING V (continued)
r ={0.2 i + 1.2 j } m
Find the moment by using the cross product.
MO =
= { -720 i + 120 j - 660 k } N·m
i j k 0.2 1.2 0 600 300 600
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GROUP PROBLEM SOLVING VI
1) Determine the position vector and the force vector
2) Determine MO = r F
Given: Strut AB exerts a force of 450 N on point B
Find: Determine the moment of the force about point O.
Plan:
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Solution:
GROUP PROBLEM SOLVING VI (continued)
MO =
= { 373 i - 99.9 j - 173 k } N·m
i j k 0 0.866 0.5 -199.82 -53.54 399.63
MO = rOB F or you can use rOA