Question

What is the maximum speed with which a 1200-kg car can round a turn of radius 90.0 m on a flat road if the coefficient of static friction between tires and road is 0.70?
2. Is this result independent of the mass of the car?

Answer 1

Answer:

78.6m/s

Explanation:

We know that frictional force also contributes to the centripetal force that keeps the car in circular motion in the turn

And is given as

F= mv²/r

But the frictional force is

F= ugm

= = 0.7*1200*9.8= 8232N

To find maximum velocity v we say

V= √F x r/m

= √ 8232* 90 /1200

= 78.6m/s

2. Yes it is independent of mass of car

Answer 2

Answer:

The value is $v = 24.85 \ m/s$

Yes

Explanation:

From the question we are told that

  The mass of the car is  $m= 1200 \ kg$

    The  radius  is $r = 90 \ m$

    The coefficient of static friction is  $\mu_s = 0.70$

Generally at maximum speed the centripetal force acting on the car is equal to the friction force on the car

So

    $F_c = F_f$

        $\frac{m v^2}{r} = \mu_s * m * g$

=>   $v = \sqrt{\mu_s * g * r }$

=>   $v = \sqrt{ 0.70 * 9.8 * 90 }$

=>    $v = 24.85 \ m/s$

Yes the value is independent of the mass because from the equation above we see that v is independent of mass