Ls 發問於 科學及數學物理學 · 4 年前

Question about moment! please answer and help thanks?

Information the mass of the car is 1200kg.

I don't understand why N cos5.

Shouldn't moment = Force x (perpendicular distance from the hinge)?

In this case, why not N (0.6+0.9) / cos5 = mg 0.9 ?

Very urgent please answer. Thank you so much

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1 個解答

  • 天同
    Lv 7
    4 年前

    I am afraid the "model answer" is wrong.

    You are right that the equation should be,

    (N1).(0.6+0.9)/cos(5) = 0.9mg

    In the model answer, only the resolved (vertical) component N1.cos(5) is considered. The other resolved (horizontal) component N1.sin(5) has been neglected.

    If the component N1.sin(5) is also taken into consideration, then the clockwise moment becomes N1.cos(5).(0.6+0.9) + N1.sin(5).y

    where y is the vertical distance between B and the horizontal line at the level of A. From geometry, tan(5) = y/(0.6+0.9), or y = 1.5.tan(5)

    Hence, the clockwise moment becomes,

    N1.cos(5).(1.5) + N1.sin(5).(1.5.tan(5))

    = 1.5(N1).cos(5) + 1.5(N1)sin(5).sin(5)/cos(5)

    = 1.5(N1)[(cos^2(5) + sin^2(5)]/cos(5)

    = 1.5(N1)/cos(5) [because cos^2(5) + sin^2(5) = 1 ]

    This is just the clockwise moment that you suggested.

    In fact, in this problem, it is not necessary to resolve the force N1 into vertical and horizontal components. This makes the calculation even more clumsy. Since N1 is already perpendicular to AB, the moment is just simply (N1).(AB)