Question

The limiting value of coefficient of friction between the road and the wheels of a car is 0.5. The maximum safe speed with which the car can take a bend of radius 5 m on a flat road is nearly :( g = 9.8 m/s^2 )​

Answer 1

Answer:

$\boxed{\mathfrak{Maximum \ safe \ speed = 4.95 \ m/s}}$

Explanation:

Limiting value of coefficient of friction ($\rm \mu$) = 0.5

Radius (r) = 5 m

Accelration due to gravity (g) = 9.8 m/s²

Maximum safe speed with which the car can take a bend:

$\boxed{ \bold{v_{max} = \sqrt{ \mu rg} }}$

By substituting value in the equation we get:

$\rm \implies v_{max} = \sqrt{0.5 \times 5 \times 9.8} \\ \\ \rm \implies v_{max} = \sqrt{24.5} \\ \\ \rm \implies v_{max} = 4.95 \: m {s}^{ - 1}$

Answer 2

Answer:

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Explanation:

In order to prevent the vehicle from slipping away on a curve, the necessary centripetal force should be provided by the force of friction between the road and the wheels of the vehicle.

Force of friction=μmg ----- here μ is the coeficient of friction(which depends on the two interacting surfaces), m is the mass of the car and g is the gravitational acceleration.

Centripetal force =  

r

m  

V

​  

 

2

 

​  

 

both should be equal. So,

μmg=  

r

m  

V

​  

 

2

 

​  

   

μ=  

rg

V

​  

 

2

 

​  

=  

400×9.8

32  

2

 

​  

=0.261.

Note that μ is a dimensionless quantity and has no unit.

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