Question

Obtain an expression of maximum velocity of vehicle on horizontal track

Answer 1

Answer:

Max speed on circular track :

Let the maximum velocity be v and radius of track be r.

Now, at limiting conditions, the centripetal force has to be equal to the maximum frictional force of the object.

F_{c} = fF

c

=f

\implies \: \dfrac{m {v}^{2} }{r} = \mu N⟹

r

mv

2

=μN

\implies \: \dfrac{m {v}^{2} }{r} = \mu (mg)⟹

r

mv

2

=μ(mg)

\implies \: {v}^{2} = \mu rg⟹v

2

=μrg

\implies \: v = \sqrt{ \mu rg}⟹v=

μrg

So, max velocity is