Question

find the maximum speed at which a car can take turn around a curve of 30m radius on a level road if the coefficient of friction between the tyres and the road is 0.4 ?​

Answer 1

Explanation:

Find the maximum speed at which a car can turn round a curve of 30 m radius on a level road if coefficient of friction between the tyres and road is 0.4. Take g = 10 m//s^(2). υ=√μrg=√0.4×30×10=√120=11m/s

Answer 2

Answer:

If a car is moving around a curve of 30m radius on a level with the coefficient of friction of 0.4 between the tyres and the road. the maximum speed at which the car can take will be  $10.95\ m/s$

Explanation:

A centripetal force is needed to turn the car which is moving around the curve. It is given by the expression

$F=\frac{mv^{2}}{r}$ ...(1)

where

r   -   radius of the curve

v   -  maximum speed of the car

m  -  the mass of the car

The centripetal force will be equivalent to the frictional force (f)

f is given by,

$f =\mu mg$  ...(2)

'μ' is the coefficient of friction.

Using (1) and (2),

$\frac{mv^{2}}{r} = \mu mg$   ...(3)

Rearranging the above equation to obtain the expression for v.

Then,

  $v^{2} = \mu rg\\ v \ = \sqrt{ \mu rg}$ ...(4)

In the question, it is given that,

r =  $30$ m

g = $10\ m/s^{2}$

$\mu = 0.40$

Substitute all these values into equation (4).

Then,

$v \ = \sqrt{ 0.40\times30\times10}$

   $= \sqrt{ 120}$

   $= 10.95\ m/s$

Maximum speed  =  $10.95\ m/s$