M1 mechanics resolving forces

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Goldenknight
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I am not sure how the picture got rotated btw. I uploaded it and it happened automatically. Sorry about that

Is there a quicker way of finding an unknown force in this? Q4 Part a I have done already and its correct but it took a whole page.

I started by finding the components of the forces given in the question at the top. Apologize for the dirty working.

I have numbered my steps from there on wards to make it easy to know.

1. I set the resultant force equation=0 for the x and y direction and made B the subject in each case

2. I divided both equations together (Sin by Cos to get Tan) to solve for the angle

3. I used the Trigonometric Identities and solved for B.

If there is any other shortcut way of doing this I would like to know. If there is also any working I got wrong or should omit also let me know

Thanks
Last edited by Goldenknight; 1 month ago
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mqb2766
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Doing it in cartesian coordinates, Id just calculate the resultant force as (x,y) and then do pythagoras to get the magnitude and atan2 to get the arg. Putting Bcos(theta), Bsin(theta) into the working throughout is unnecessary?

Note, the question seems to have values chosen to make a cos/sin rule approach a potential solution as well.
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T!gger34
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Once you have found there, you could plug that back into one of your first two resolving forces equations to find B without bothering with the somewhat long winded trig identity.

Other than that, you may wish to save time and space by simply writing R(->) instead of "resolving in a horizontal direction", etc.
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