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Math Help - Please help with Resultant of Force Question

  1. #1
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    Please help with Resultant of Force Question

    I am in a Applied Mechanics for Engineering Course and need some help with vectors. I am struggling with this question and would like some help. How do I solve this? I am also very confused with how the Force of 68N shows an angle of (x=15, y=8) and not the angle. Can someone please explain this to me? I have drawn a picture in paint:

    Question:
    Determine the resultant of the force system shown




    Any help would be greatly appreciated
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  2. #2
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    Hello system32
    Quote Originally Posted by system32 View Post
    I am in a Applied Mechanics for Engineering Course and need some help with vectors. I am struggling with this question and would like some help. How do I solve this? I am also very confused with how the Force of 68N shows an angle of (x=15, y=8) and not the angle. Can someone please explain this to me? I have drawn a picture in paint:

    Question:
    Determine the resultant of the force system shown




    Any help would be greatly appreciated
    First, the meaning of the (x=15, y=8) direction is that the force of 68 N makes an angle \arctan(\tfrac{8}{15}) with the x-direction. You can work out this angle in degrees if you like, but you don't need to. The hypotenuse of the triangle is \sqrt{8^2+15^2}=17 exactly. So the sine of the angle is \frac{8}{17} and its cosine is \frac{15}{17}.

    Now, to find the resultant force, add up their x- and y-components, taking x as positive to the right, and y positive upwards, using sines and cosines as appropriate. I'll do the x one for you:

    X=-80\cos65 -50\sin15+68\times\frac{15}{17}=13.25, where X is the x-component of the resultant force.

    Do the same for Y, the sum of the y-components.

    Then, using a right-angled triangle with sides X and Y work out the magnitude of the resultant, using \sqrt{X^2+Y^2} and the angle the resultant makes with the x-direction, which is \arctan\Big(\frac{Y}{X}\Big).

    Grandad
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  3. #3
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    thank you
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