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A car of mass m is moving with a velocit...

A car of mass m is moving with a velocity v over a bridge. What will be the values of the force F at the highest point of a convex bridge and at the lowest point of a concave bridge?

Text Solution

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A centripetal force is required to move the car over a convex bridge. The value of this centripetal force is ` (mv^(2))/(r )`.
Here, r is the radius of curvature of the convex bridge
At the highest point of the bridge. The resultant of the weight of the car mg and F will supply the necessary centripetal force.
`therefore " " mg - F = (mv^(2))/(r )`
or,` " " F = m(g- (v^(2))/(r))`

(ii) A centripetal force is required to move the car over concave bridge also. At the lowest point of the concave bridge, the resultant of the weight of the car mg and f will supply the necessary centripetal force.
`therefore" " F - mg = (mv^(2))/(r ) " " or, f = m(g + (v^(2))/(r))`
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