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two identical cars, one on the moon and one on the earth, have the same speed and are rounding banked turns that have the same radius r. there are two forces acting on each car, its weight mg and the normal force $f_n$ exerted by the road. recall, that the weight of an object on the moon is about one sixth of its weight on earth. how does the centripetal force on the moon compare with that on earth?
the centripetal forces are the same.
the centripetal force on the moon is greater than that on the earth.
the centripetal force on the moon is less than that on the earth.
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Explanation:

Step1: Recall centripetal - force formula

The centripetal force $F_c$ for a car moving on a banked - turn is provided by the horizontal component of the normal force and the horizontal component of the weight. The centripetal - force formula for a car on a banked turn is $F_c = m\frac{v^{2}}{r}$, where $m$ is the mass of the car, $v$ is the speed of the car, and $r$ is the radius of the turn.

Step2: Analyze given conditions

We are given that the two cars are identical (so they have the same mass $m$), they have the same speed $v$, and they are rounding banked turns with the same radius $r$.

Step3: Determine centripetal - force relationship

Since $F_c = m\frac{v^{2}}{r}$ and $m$, $v$, and $r$ are the same for both cars (one on Earth and one on the Moon), the centripetal forces are the same.

Answer:

The centripetal forces are the same.