EXAMPLE 3.2.2: RESULTANT OF SPATIAL FORCES

The rope attached to the walls at points A and B is pulled by a man exerting 70 lb. Express force FA and FC as Cartesian vectors. Determine the magnitude and coordinate direction angles of the resultant force acting at B.

With the exerted force of the man = 70lb, both  and . It would be easier to determine the forces' Cartesian vectors if you can determine the coordinates of the points included.

POINT	i, ft	j, ft	k, ft
A	5.00	7.00	5.00
B	-1.00	5.00	8.00
C	5.00	7.00	4.00

FOR FORCE FA

Determine the Cartesian vector of Force FA by taking the difference of points A and B's coordinates. Take the convention sign of the axes to identify if you are to use + or - in the equation.

At x-axis, for i: 5 - (-1) = 6ft (the force direction going to +x) thus +6i

At y-axis, for j:-7-(-5)   = -2ft (the force directing to -y) thus -2j

At z-axis, for k: 8- 5     = 3 ft (the force going downwards) thus -3k

Giving us the vector

The scalar of which is

So, the Cartesian vector of FA:



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FOR FORCE FC

Similar with FA,





For which the scalar of FC becomes:



Then, the Cartesian vector of FC is







RESULTANT

MAGNITUDE:

FORCE	i	j	k
FA	60.00	-20.00	-30.00
FC	30.00	60.00	-20.00
summation	90.00	40.00	-50.00

                                                                   

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INCLINATION:





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