Question

When a car rounds a curve on a flat road what supplies the centripetal force that keeps the car moving in a circular path? Establish the formula for the maximum safe speed of the car.​

Answer 1

Answer:

the frictional force provide the required centripetal force for the car

the two force should be equal in magnitude

so

Ff=Fc

uR= mv²/r

u= coefficient of friction

R=w=reaction force

m=mass

v=linear speed

r=radius

so

mgu=mv²/r

and

v=under root ugr

Answer 2

When car goes round a curved road, FRICTION supplies the centripetal force. This prevents the car from going out of the road.

Let maximum safe speed be v :

$\therefore \: F_{c} = f$

$\implies \: \dfrac{m {v}^{2} }{r} = f$

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

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

$\implies \: \dfrac{ {v}^{2} }{r} = \mu g$

$\implies \: {v}^{2} = \mu rg$

$\implies \: v = \sqrt{ \mu rg}$

So, max safe speed is:

$\boxed{ \bf\: v = \sqrt{ \mu rg} }$