Three ropes are attached to a crate and exert the forces shown. Given /alpha = 3

Question

Three ropes are attached to a crate and exert the forces shown. Given /alpha = 30/degrees, if the forces are to be replaced with a single equivalent force applied at point AB, determine

a) the total forcce of the three ropes R=Rxi+Ryj=F1+F2+F3. Give its components, magnitude |R|, and directional angle between R and the x axis.

b) the total moment of the 3 forces about point A, MA

c) Find the distance dx from A the point of application of for R in order to create the same moment about A, MA.

d) If a single force R1=R1j is going to be applied at point B to create the same moment MA what is the value of R1?

e) If the other two forces remain unchanged, what is the angle /alpha to create the same Rj?

Explanation / Answer

F1=-100cos30 i +100sin30 j, F2=160j, F3=400sin25 i +400cos25j a). R=82.44i+572.52j angle with x axis=tanh(572.52/82.44)=81.80 degrees b). moment of F1 about A will be zero MA=0+160*0.46 k+362.52*0.66 k+169.047*0.26 k=356.81 k c).moment of R(Ri +Rj) about A If we apply R on line AB then Ri wont give any moment because it is passing through point itself(no perpendicular distance) Rj*dx=356.81 dx=356.81/572.52=0.623m=62.3cm d).Rj*0.66=Ma Rj=356.81/0.66=540.62N e).F1sin(alpha)+F2+F3cos25=540.62 sin(alpha)=0.181 alpha=10.43degrees

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