Answer:
A. 325.4 N
Explanation:
At the bottom of the swing, the net force is equal to:
[tex]F_{net}=T-mg=ma[/tex]
Where T is the tension, m is the mass, g is the gravity, and a is the centripetal acceleration, so a = v²/r. With v the speed and r is the length of the swing. So, solving for T, we get:
[tex]\begin{gathered} T-mg=m\frac{v^2}{r} \\ \\ T=m\frac{v^2}{r}+mg \end{gathered}[/tex]
Now, we can replace m = 27 kg, v = 3 m/s, r = 4 m, and g = 9.8 m/s² to get
[tex]\begin{gathered} T=(27\text{ kg\rparen}\frac{(3\text{ m/s\rparen}^2}{4\text{ m}}+(27\text{ kg\rparen\lparen9.8 m/s}^2) \\ \\ T=60.75\text{ N + 264.6 N} \\ T=325.4\text{ N} \end{gathered}[/tex]
Therefore, the answer is
A. 325.4 N
