# Q:- There is a parabolic shaped bridge across a river of width 100 m. The highest point of the bridge is 5 m above the level of the banks. a car of mass 1000 kg is crossing  the bridge at a constant speed of 20 m/s. Using the notation indicated in the figure find the force exerted on the bridge by the car when it is at the highest point of the bridge.(g=10 m/s^2)        ans:-8.40 kN

148 Points
12 years ago

Dear Taparsranjan

first find out the equation of parabola

let highest point is  origin. so equation of parabola : x2=-ay (opening downward)

point( 50,-5) will lie on parabola

so a will come a=500

x2=-500y

now differentiate

2x=-500 dy/dx          so dy/dx at x=0  is 0

and 2= -500d2y/dx2   so d2y/dxat x=0 is -1/250

radius of curvature at x=0 of parabola

1/R  = d2y/dx2  /[ 1+(dy/dx)2]3/2

R= 1/d2y/dx2

= 250

force on bridge at highest point = mg-mv2/R

=1000 * 10  - 1000*(20)2/250

=8.4 kN in the downward  direction

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