Respuesta :
Answer:
c. 0.816
Explanation:
Let the mass of car be 'm' and coefficient of static friction be 'μ'.
Given:
Speed of the car (v) = 40.0 m/s
Radius of the curve (R) = 200 m
As the car is making a circular turn, the force acting on it is centripetal force which is given as:
Centripetal force is, [tex]F_c=\frac{mv^2}{R}[/tex]
The frictional force is given as:
Friction = Normal force × Coefficient of static friction
[tex]f=\mu N[/tex]
As there is no vertical motion, therefore, [tex]N=mg[/tex]. So,
[tex]f=\mu mg[/tex]
Now, the centripetal force is provided by the frictional force. Therefore,
Frictional force = Centripetal force
[tex]f=F_c\\\\\mu mg=\frac{mv^2}{R}\\\\\mu=\frac{v^2}{Rg}[/tex]
Plug in the given values and solve for 'μ'. This gives,
[tex]\mu = \frac{(40\ m/s)^2}{200\ m\times 9.8\ m/s^2}\\\\\mu=\frac{1600\ m^2/s^2}{1960\ m^2/s^2}\\\\\mu=0.816[/tex]
Therefore, option (c) is correct.
