Question

) A 1000-kg car is moving at 30 m/s around a horizontal unbanked curve whose diameter is 0.20 km. What is the magnitude of the friction force required to keep the car from sliding?

Answer 1

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:

$F_f = m \frac{v^2}{r}$

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

$r=\frac{0.20 km}{2}=0.10 km = 100 m$ (since the diameter is 0.20 km, the radius is half that value)

And substituting, we find

$F_f = (1000) \frac{30^2}{100}=9000 N$

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