1) (10 points total) A bracket is cantilevered from a floor at point \"O as show
ID: 2305490 • Letter: 1
Question
1) (10 points total) A bracket is cantilevered from a floor at point "O as shown. A force with a magnitude of F56Nis applied at point "A and directed toward point "D". F-56N 1 m sm a) (2 points) Express the force, F, as a Cartesian vector (i.e. F). Note the orientation of the axis system. b) (4 points) Determine the moment of force F about point "O": (i.e. Mo-?) Express you answer as a Cartesian vector. (4 points) Determine the magnitude of projection of force F along axis "AO: (i.e. a line running in the direction from A" to O) c)Explanation / Answer
location of point A = (-1.5,3,1)
location of point D = (0,0,2)
vector form point A to d = (0- (-1.5))i + (0-3)j + (2-1)k
V= 1.5i -3j +k
unit vector from point A to D = V/|V|
|V| = (1.52 +32 +12)1/2
=3.5
unit vector from A to D = (1.5i -3j +k)/3.5
magnitude of force |F| =56
F = |F|* unit vector from A to D
=56/3.5 * (1.5i -3j +k)
F=24i - 48j +16k -----------------answer for part (a)
b) moment of force = r X F (cross product)
where r is the vector pointing from the origin to point A
r = -1.5i +3j +k
F = 24i - 48j +16k
vector product = (-1.5i +3j +k) x(24i - 48j +16k)
= (3*16 - 1*(-48))i + (1*24 - (-1.5)*(16))j + ((-1.5)*(-48) - (3)(24))k
=96i +48j +0k
moment about O = 96i +48j ----answer for part (b)
c) magnitude of projection is given by the sclar projeciton of vector a on b
scalar projection of a on b = a.b/|b|
the line running from A to O has vector will be just negative of what vector we found from o to A.
rAO = 1.5i -3j -k
| rAO| = (1.52 +32+12)1/2 =3.5
F.r = (24i - 48j +16k)(1.5i -3j -k) = 24*1.5 + (-48)(-3) +(16)(-1)
= 36 + 144 - 16
F.r =164
magnitude of projeciton vector = 164/3.5 = 46.85N
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