Question

A rock in a sling is swung around in a circle.
How would the centripetal force change if the rock was 8 times lighter??

How would the centripetal force change if the rock was swung 7 times faster?


How would the centripetal force change if the sling was 6 times longer?

Answer 1

The centripetal force equals $F = ma_{c} = mro^{2} = \frac{mv^{2}}{r}$.

a) If the rock will 8 times lighter, than its mass will equal: $\frac{m}{8}$. So, we can find the centripetal force in this case: $F_{1} = \frac{m}{8} \cdot \frac{v^{2}}{r} = \frac{1}{8} \cdot \frac{mv^{2}}{r} = \frac{1}{8} \cdot F$. So, the centripetal force will be lower in 8 times than it was if the rock will 8 times lighter.

Answer: lower in 8 times.

b) If the rock will swung 7 times faster than its velocity will be equal $7 \cdot v$. So, we can find the centripetal force in this case: $F_{2} = \frac{m(7v)^{2}}{r} = 49 \cdot \frac{mv^{2}}{r} = 49 \cdot F$. So, it will be greater in 49 times.

Answer: greater in 49 times.

c) If the sling will be 6 times longer than the radius of this circular motion will be 6 times greater and equals $6 \cdot r$. So, we can find the centripetal force in this case: $F_{3} = \frac{mv^{2}}{(6 \cdot r)} = \frac{1}{6} \cdot \frac{mv^{2}}{r} = \frac{1}{6} \cdot F$. So, it will be 6 times lower.

Answer: lower in 6 times.