The frictional force required is 9000 N
Explanation:
In order to keep the car in the turn in circular motion without sliding, the frictional force must provide the centripetal force necessary for the circular motion.
Therefore, we can write:
[tex]F_f = m \frac{v^2}{r}[/tex]
where the term on the left is the frictional force while the term on the right is the centripetal force, and where:
m is the mass of the car
v is its speed
r is the radius of the curve
For the car in this turn, we have
m = 1000 kg
v = 30 m/s
[tex]r=\frac{0.20 km}{2}=0.10 km = 100 m[/tex] (since the diameter is 0.20 km, the radius is half that value)
And substituting, we find
[tex]F_f = (1000) \frac{30^2}{100}=9000 N[/tex]
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