Question

derive the equation for upper limit of the speed for a vehicle at the top of convex bridge.​

Answer 1

Suppose a vehicle moves on a convex bridge

• Then

$\\\qquad\quad\boxed {\red{\sf\longrightarrow Centipetral\;force=mg\:cos\theta -\dfrac {mv^2}{r}} }$

$\\\qquad\quad\boxed {\purple{\sf\longrightarrow Reaction_{(R)}=mg\:cos\theta-mv^2}}$

• where
• m=mass of vehicle
• g=acceleration due to gravity
• R=reaction
• v=velocity

Diagram:-

$\setlength{\unitlength}{1cm}\begin{picture}(0,0)\thicklines\qbezier (0,0)(2.5,2.5)(5,0)\put (2.5,-0.5){\circle*{0.2}}\qbezier (2.5,-0.5)(2.5,-0.5)(1,1.5)\put (1,1.5){\vector (-1,1){0.4}}\put(1.4,1){\vector (1,-4){0.3}}\put (1.55,0.4){\sf \theta }\thinlines\qbezier (2.5,1.3)(2.5,1.3)(2.5,-0.5)\put (0.2,1.8){\sf R}\put (0.6,1){\framebox(1,0.5){\bf car}}\put(1,0.1){\sf mg}\put (2,0.5){\sf mg\:cos\theta }\put (2.3,-0.3){\bf \theta }\put (1.6,0.9){\bf v}\put (1.5,-1){\sf Convex\:Bridge}\end{picture}$

Centipetral Force:-

• When a object moves on a circular path then a net force is acted on the object to keep it moving along the circular direction. It is called centipetral force .

$\boxed{\blue{\sf {}^{F}Centipetral=m\dfrac {v^2}{r}}}$

• According to Newton's First law A object keep moving on a straight path until it is acted on by external force (Centipetral force).

Note:-

• View the diagram on web .

Hope my diagram looks good :)