Question

Is it safe to drive your 1600-kg car at speed 34 m/s around a level highway curve of radius 190 m if the effective coefficient of static friction between the car and the road is 0.50?

Answer 1

Answer:

It is unsafe

Explanation:

v = Velocity of car = 34 m/s

r = Radius of turn = 190 m

$\mu$ = Coefficient of static friction = 0.5

m = Mass of car = 1600 kg

g = Acceleration due to gravity = 9.81 m/s²

The centripetal force is given by

$F_c=m\frac{v^2}{r}\\\Rightarrow F_c=1600\frac{34^2}{190}\\\Rightarrow F_c=9734.73\ N$

The frictional force is given by

$F_f=\mu mg\\\Rightarrow F_f=0.5\times 1600\times 9.81\\\Rightarrow F_f=7848\ N$

If the centripetal force is greater than the frictional force then the car will slip which makes it unsafe.

Here, the centripetal force is greater than the frictional force which makes it unsafe to drive it at that speed.