Question

Suppose you have an object tied to a rope and are rotating it over your head in uniform circular motion. What would have to do to the rope length in order to cut the centripetal force in half

Answer 1

Answer:

We must duplicate the length of the rope (R'=2R) to get

$F'=\frac{1}{2}F$

Explanation:

The equation of the centripetal force is given by:

$F_{c}=ma_{c}$

$F_{c}=m\frac{v^{2}}{R}$

Where:

R is the length of the rope

m is the mass of the object

v is the speed of the object

If we want to reduce the centripetal force in half, we can duplicate the length of the rope (R'=2R), which means:

$F'_{c}=m\frac{v^{2}}{R'}$

$F'_{c}=m\frac{v^{2}}{2R}$

$F'_{c}=\frac{1}{2}F_{c}$

I hope it helps you!