Question

motorcycle has to move with a constant speed on an
overbridge which is in the form of a circular are of radius
R and has a total length L. Suppose the motorcycle
starts from the highest point. (a) What can its maximum
velocity be for which the contact with the road is not
broken at the highest point ? (b) If the motorcycle goes
at speed 1/
$\sqrt{2}$
times the maximum found in part (a),
where will it lose the contact with the road ? (c) What
maximum uniform speed can it maintain on the bridge
if it does not lose contact anywhere on the bridge ? if you know the answer then only write the answer.​

Answer 1

Answer:

According to the figure we can see that,

R is the radius of the bridge and L is the total length of the bridge

a) Now at highest point ,

mg = mv^2/R or, v = √Rg

b) Now for this case v = 1/√2√Rg is given

Let it loses the contact at point p,

Therefore at point p  mgcostheta = mv^2/R

                                 => v^2 = Rgcostheta

                                    => (√Rg/2)^2 = Rgcostheta

                                      => Rg/2 = Rgcostheta

                                    => costheta = 1/2 = 60 degree = π3

Now we can say that theta = l/r = l = r theta = πR/3

Hence it losses contact at πR/3 distance from the highest point.