Answer:
The fastest rotational speed of the mass is [tex]3.536s^{-1}[/tex].
Explanation:
Here the string's breaking strength of 50.0 N means that the centripetal force exerted on the 5.00kg mass cannot exceed 50.0N—if it does, the string would break.
Therefore, we demand that
[tex](1).\;\: \dfrac{mv^2}{R} = 50.0N[/tex]
where [tex]m = 5.00kg[/tex], [tex]R = 0.800m[/tex] is the radius of the circle (also the length of the string), and [tex]v[/tex] is the tangential velocity of the mass.
Now, the tangential velocity can be written in terms of the rotational speed [tex]\omega[/tex] as follows:
[tex](2).\;\: v = \omega R[/tex],
and putting that into equation (1) we get:
[tex]\dfrac{m(\omega R )^2}{R} = 50.0N[/tex]
[tex]m \omega^2 R = 50.0N[/tex],
and we solve for the rotational speed [tex]\omega[/tex] to get:
[tex]\omega = \sqrt{\dfrac{50N}{mR} }.[/tex]
Finally, we out in the numeral values and get;
[tex]\omega = \sqrt{\dfrac{50N}{(5.00kg)(0.800m)} }.[/tex]
[tex]\boxed{\omega = 3.536s^{-1}}[/tex]
which is the fastest rotational speed of the mass.
