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Question

A car of mass m=1000 kg is moving with constant speed v=10 m/s on a parabolic shaped bridge AFOE of span l=40 m and height h=20 m as shown in the figure. Then the net force applied by the bridge on the car, when it is at point F is :

Assume g=10 ms2

A
500052 N
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B
50002 N
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C
100002 N
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D
500025 N
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Solution

The correct option is A 500052 N
Taking the origin at O and OC as y-axis equation of bridge is
y=x220
So, slope at F=tanθ=dydx=2x20=2×1020=1
At point F,
mgcosθN=mv2R
mg12N=mv2R

N=mg2mv2R and fs=mgsinθ=mg2
Radius of curvature at F, R=(1+(dydx)2)32d2ydx2=(1+1)3/2110=202(metre)

N=10m2100m202=5m2
fs=10m2
Net force=m252+1002=5m52=500052N

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