Answer:
782.58 N
Explanation:
By the second law of Newton, at the bottom of the swing path, the net force is equal to
[tex]\begin{gathered} F_{net}=T-mg=ma \\ \\ T-mg=m\frac{v^2}{r} \end{gathered}[/tex]Since a is the centripetal acceleration, we get that a = v²/r. Where v is the speed and r is the length of the hair.
Solving for the tension T, we get:
[tex]T=m\frac{v^2}{r}+mg[/tex]Now, we can replace m = 51 kg, v = 6.5 m/s, g = 9.8 m/s² and we can convert r = 25 feet to meters as
[tex]25\text{ feet}\times\frac{1\text{ m}}{3.281}=7.62\text{ m}[/tex]Then, the tension is equal to
[tex]\begin{gathered} T=(51\text{ kg\rparen}\frac{(6.5\text{ m/s\rparen}^2}{7.62\text{ m}}+(51\text{ kg\rparen\lparen9.8 m/s}^2) \\ \\ T=782.58\text{ N} \end{gathered}[/tex]Therefore, the tension is 782.58 N
