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27 October, 13:30

Forces with magnitudes of 2000 newtons and 900 newtons act on a machine part at angles of 10° and 85° respectively, with the x-axis. find the direction and the magnitude of the resultant of these forces. round to the nearest tenth place.

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  1. 27 October, 14:02
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    First, you need to find the components of each force:

    F₁x = 2000 cos10 = 1969.6 N

    F₁y = 2000 sin10 = 347.3 N

    F₂x = 900 cos85 = 78.4 N

    F₂y = 900 sin85 = 896.6 N

    Then, you have to sum up the same components of the two forces:

    Rx = F₁x + F₂x = 1969.6 + 78.4 = 2048.0 N

    Ry = F₁y + F₂y = 347.3 + 896.6 = 1243.9 N

    In order to find the magnitude of the resultant, you need to apply the Pythagorean theorem:

    R = √ (Rx² + Ry²)

    = √ 2048.0² + 1243.9²

    = 2396.2 N

    Now, in order to find the direction (angle), you need to use a bit of trigonometry:

    α = tan⁻¹ (Ry / Rx)

    = tan⁻¹ (1243.9 / 2048)

    = tan ⁻¹ (0.60737)

    =31.3°

    Therefore, the answer is: the resultant has a magnitude of 2396.2N with an angle of 31.3° with respect to the x-axys.
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