Answer:
22.3 N
Explanation:
The centripetal force acting on a the rock is given by:
[tex]F=m\frac{v^2}{r}[/tex]
where
m = 3.0 kg is the mass of the rock
v is the speed of the rock
r = 0.75 m is the radius of the trajectory
We need to find the speed of the rock. We know that the rock makes a complete circle in t = 2.0 s, and the radius of the circle is r = 0.75, so the speed is equal to the ratio between the distance covered (the perimeter of the circle) and the time taken:
[tex]v=\frac{2 \pi r}{t}=\frac{2 \pi (0.75 m)}{2.0 s}=2.36 m/s[/tex]
And so, the centripetal force is
[tex]F=m\frac{v^2}{r}=(3.0 kg)\frac{(2.36 m/s)^2}{0.75 m}=22.3 N[/tex]
