If the resultant force acting on the bracket is to be directed along the positiv

Question

If the resultant force acting on the bracket is to be directed along the positive u axis, and the magnitude of

F1 is required to be minimum, determine the magnitude of the resultant force. Then determine the magnitude of F1

Step by step solutions would be awesome, I cant find any real help online and this is a online course. Thanks.!

If the resultant force acting on the bracket is to be directed along the positive u axis, and the magnitude of F1 is required to be minimum, determine the magnitude of the resultant force. Then determine the magnitude of F1

Explanation / Answer

writing forces in terms of components

F3 = 500 cos 45 i - 500 sin 45 j =353.55 i -353.55 j

F2=-650 *3/5 i +650*4/5 j =-390i +520 j

F1 be F(cos? i +sin? j )

adding all we get (Fcos?-36.45) i + (Fsin?+166.45) j

for it to be in 45 degrees x component should be equal to y component(arctan(y/x)=1 for 45 degrees)

so

Fcos?-36.45=(Fsin?+166.45)

Fcos?=Fsin?+202.9

F(cos ? -sin ?) =202.9

for F to be min cosx-sinx should be max

max of cosx - sin x is ?2 at ?=-45 (differentiate it and find critical points you will get it)

F=202.9/?2 =143.47 N

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