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Math Help - Forces as a Vectors

  1. #1
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    Forces as a Vectors

    Find the horizontal and vertical components of each of the forces:

    f) 36N acting vertically

    {\overrightarrow {r} } = (0, 36sin \theta)

    How do I find the y value for the component if I cannot solve for 36sin \theta?



    Find the resultant of each pair of forces acting on an object.

    d) forces of 7N east and 12N north

    \sqrt {|{\overrightarrow {r} }|^2} = \sqrt{7^2 + 12^2}
    |{\overrightarrow {r} }| = 13.9


    tan \theta = \frac {12}{7}
    \theta = 60

    Therefore, 13.9N, _____________ (How do I find the direction of this force? Can you please show me how using a diagram?)

    e) forces of 6N southwest and 8N northwest

    My Answer: 10N, N8W --------- is my answer correct?

    g) forces of 6N southeast and 8N northwest

    My Answer: 2N, N45W ---------------- is my answer correct?
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    Forum Admin topsquark's Avatar
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    Quote Originally Posted by Macleef View Post
    Find the horizontal and vertical components of each of the forces:

    f) 36N acting vertically

    {\overrightarrow {r} } = (0, 36sin \theta)

    How do I find the y value for the component if I cannot solve for 36sin \theta?
    You are over-thinking it. The vector is vertical, hence it is acting entirely in the y direction. So the vector is (0, 36). (If you want, \theta = 90^o.)

    -Dan
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    Forum Admin topsquark's Avatar
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    Quote Originally Posted by Macleef View Post
    Find the resultant of each pair of forces acting on an object.

    d) forces of 7N east and 12N north

    \sqrt {|{\overrightarrow {r} }|^2} = \sqrt{7^2 + 12^2}
    |{\overrightarrow {r} }| = 13.9


    tan \theta = \frac {12}{7}
    \theta = 60

    Therefore, 13.9N, _____________ (How do I find the direction of this force? Can you please show me how using a diagram?)
    You pretty much have it.

    Add them by components:
    Using the usual xy coordinate plane, the first is (7, 0) and the second is (0, 12). So the resultant vector will be (7 + 0, 0 + 12) = (7, 12).

    So the magnitude is r = \sqrt{7^2 + 12^2} = 13.892443989 and the angle (in the first quadrant, since the x and y components are both positive) will be 59.743562836 degrees. (Or 60. degrees N of E.)

    -Dan
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