Ch2 Main Ideas

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

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:

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:

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:

Ch3 Main Ideas

Ch4 Main Ideas

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:

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

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:

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