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Math Help - Rotational Equilibrium

  1. #1
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    Rotational Equilibrium

    Whilst I'm usually decent at physics this chapter seems to go right over my head. The book problems right now are

    "A uniform bridge 20.0m long and weighing 4.00 x 10^5 N is supported by two pillars located 3.00m from each end. If a 1.96 x 10^4 N car is parked 8.00m from one end of the bridge, how much force does each pillar exert?"

    I have no idea where to start. They give me a few equations earlier in the chapter but those are all about rotation, and there seems to be no rotation in this problem. I don't exactly know how I'd draw a force diagram here. I know mg, normal force, and all but I'm not sure how I'd find how much force is exerted on each pillar.

    Thanks.
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  2. #2
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    Quote Originally Posted by MBrown92 View Post
    Whilst I'm usually decent at physics this chapter seems to go right over my head. The book problems right now are

    "A uniform bridge 20.0m long and weighing 4.00 x 10^5 N is supported by two pillars located 3.00m from each end. If a 1.96 x 10^4 N car is parked 8.00m from one end of the bridge, how much force does each pillar exert?"

    I have no idea where to start. They give me a few equations earlier in the chapter but those are all about rotation, and there seems to be no rotation in this problem. I don't exactly know how I'd draw a force diagram here. I know mg, normal force, and all but I'm not sure how I'd find how much force is exerted on each pillar.

    Thanks.
    let F_1 = upward pillar force near the left end of bridge
    F_2 = upward pillar force near the right end of bridge
    W_B = bridge weight
    W_C = car weight

    let the car be 8 m from the left end


    translational equilibrium ...

    \sum F_y = 0

    F_1 + F_2 - W_B - W_C = 0



    let the point where F_1 exerts its upward force be the pivot point for system torques.

    rotational equilibrium ...

    \sum \tau = 0

    F_2(14 \, m) - W_C(5 \, m) - W_B(7 \, m) = 0

    solve for F_2 ... then determine F_1
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