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Math Help - vector forces

  1. #1
    Newbie sir nerdalot's Avatar
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    vector forces

    Hello!!

    I just need some help with these two questions regarding vector forces...
    1. A body with a weight of 100 N is placed on a smooth incline. The normal reaction force of the incline on the body is 85 N. A rope is attached to the body and applies a force of 50 N parallel and up the incline. Describe what will happen to the body. That is will it stay at rest, move up the incline or slide down the incline? Justify your answer with calculations.

    2. A body with weight 40 N is placed on a smooth plane inclined at an angle of 60 degrees to the horizontal. A horizontal force, F, is applied to the body. Find the magnitude of F if it is sufficient to hold the body at rest
    Thankyou in advance for the help!!
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  2. #2
    MHF Contributor
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    1. A body with a weight of 100 N is placed on a smooth incline. The normal reaction force of the incline on the body is 85 N. A rope is attached to the body and applies a force of 50 N parallel and up the incline. Describe what will happen to the body. That is will it stay at rest, move up the incline or slide down the incline? Justify your answer with calculations.

    So we find all the forces parallel to the incline.

    Due to the body,
    B = sqrt[(100)^2 -(85)^2] = 52.68N going down.

    Due to rope,
    R = 50N going up.

    The B is greater than the R, so the body will slide down the incline. ----answer.

    --------------------------------------------

    2. A body with weight 40 N is placed on a smooth plane inclined at an angle of 60 degrees to the horizontal. A horizontal force, F, is applied to the body. Find the magnitude of F if it is sufficient to hold the body at rest

    We find again all forces parallel to the incline.
    I assume you know how to draw the diagram.

    Due to the body,
    B = 40sin(60deg) = 34.64N going down

    Due to Hrizontal force F,
    P = Fcos(60deg) = 0.5F going up

    For the body not move,
    0.5F = 34.64N
    F = (34.64N)/0.5 = 69.28N ----------------answer.
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