1) Available force of friction: 6174 N
2) No
Explanation:
1)
The magnitude of the frictional force between the car's tires and the pavement of the road is given by
[tex]F_f=\mu mg[/tex]
where
[tex]\mu[/tex] is the coefficient of friction
m is the mass of the car
g is the acceleration of gravity
For the car in this problem, we have:
[tex]\mu=0.500[/tex] (coefficient of friction)
m = 1260 kg (mass of the car)
[tex]g=9.8 m/s^2[/tex]
Therefore, the force of friction is
[tex]F_f=(0.500)(1260)(9.8)=6174 N[/tex]
2)
In order to mantain the car in circular motion, the force of friction must be at least equal to the centripetal force.
The centripetal force is given by
[tex]F=m\frac{v^2}{r}[/tex]
where
m is the mass of the car
v is the tangential speed
r is the radius of the curve
In this problem, we have
m = 1260 kg
[tex]v=54.1 km/h =15.0 m/s[/tex] is the tangential speed
r = 41.6 m is the radius of the curve
Therefore, the centripetal force is
[tex]F=(1260)\frac{15.0^2}{41.6}=6814 N[/tex]
Therefore, the force of friction is not enough to keep the car in the curve, since [tex]F_f<F[/tex]
