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Tapasranjan Das Grade: 12
        

6725-1674_9902_untitled.bmp


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 

7 years ago

Answers : (1)

Badiuddin askIITians.ismu Expert
147 Points
										

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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Badiuddin

7 years ago
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