1a) Determine the magnitude and direction of the resultant...

1a) Determine the magnitude and direction of the resultant force mathematically with the three forces on the ring shown below: 1b) Draw a graph of the vector addition of the three forces using the head to tail method clearly showing the resultant vectors magnitude and direction graphically. y F\(_2\)=800N 600 ( F\(_1\)=600N 450 x F\(_3\)=450N 750

Transcript

00:01 Let's summarize the given question as this image is given in the question.

00:06 So we are given with the three forces.

00:09 If let the other two forces, f1, okay, besides f1, let the other two forces, f2 and f3, got it.

00:17 So we have to tell out, we are basically theta value of theta.

00:21 So let's, and in second case, if suppose f1 is equal to 500 and theta is equal to 20 degrees, so we have to tell out that what is the resultant force acting on it so let's see so in x direction we can start in the net force is zero y because in quotient it is given that the resultant is along the y -axis only so so net force is equal to zero which means that 400 cost 30 degree is equal to f1 sine theta is equal to f3 sine alpha because why because there is a canceling effect because this direction force will cancel with this direction then only the net force can be zero so there is a canceling effect now it becomes 400 root 3 f1 sine theta which is going to 600 into multiplied by 600 multiplied by cost 3 and why is cause because of cause thing okay and why f1 is signed because f1 is signed f1 is signed because the so the it will become so our answer will become 133 newton so now in wide direction fi is given as 800 okay so if i is given as 800 newton so now if we see the component then it is f2 sine 30 degree plus f1 sine 30 plus 3 that is now if we see that it is f1 cost 3 theta plus f2 sine theta 30 degrees and f3 is equal to sine alpha which is it is the value of sine alpha is given okay so we will take it from the direction of the sides so it will f1 cos theta plus 600 to 3 by 5 as given it's a f3 and sine alpha and f2 is a 5 1 by 2 so it will be 800 newton so f1 cos the 3 theta is equal to 240 newton so equation 1 will be the first equation in x direction and it is in sign.

02:44 So if we know that for the magnitude, we will take the square root of summation of cos square and sine square component of.

02:56 So it becomes like the magnitude 133 into it comes to 174 .6 newton...

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