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Calculate the ratio of the reaction of a convex bridge at the highest point of the reaction of the concave bridge at its lowest point when a car passes at 30 km/hr and the radius of either bridge is 20m

Calculate the ratio of the reaction of a convex bridge at the highest point of the reaction of the concave bridge at its lowest point when a car passes at 30 km/hr and the radius of either bridge is 20m

Grade:12

1 Answers

Arun
25750 Points
6 years ago
Dear Student
 
The forces acting on the car are weight mg  and normal reaction from the road on the bridge.  We ignore friction and Thrust force of engine for this calculation.  As the car is moving at uniform speed, friction and engine thrust are equal and opposite. They are perpendicular to radius and so  do not contribute to the centripetal force. 

        v = 30 kmph = 25/3 m/s

1) Convex: centripetal force :
           mg - N1 = m v² / R       =>  N1 = m (g - v^2/R) = m*235/36 N

2) Concave bridge:  
          N2 - mg = m v²/R      =>  N2 = m (g + v²/R) = m *485/36  N

Ratio:   N1/ N2 = 235/485 = 47/97
 
Regards
Arun (askIITians forum expert)

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