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*Question:* A truck of mass
is crossing
a uniform horizontal bridge of mass
and length
.
The bridge is supported at its two end-points. What are the reactions
at these supports when the truck is one third of the way across the bridge?

*Answer:* Let and be the reactions at the bridge supports.
Here, is the reaction at the support closest to the truck. Setting the net vertical
force acting on the bridge to zero, we obtain

Setting the torque acting on the bridge about the left-most support to zero,
we get

Here, we have made use of the fact that centre of mass of the bridge lies at its
mid-point. It follows from the above two equations that

and

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Richard Fitzpatrick
2006-02-02