Question

What is the tension in the swing’s chain at this time?

Answer 1

A. 325.4 N

Step-by-step explanation:

At the bottom of the swing, the net force is equal to:

`F_(net)=T-mg=ma`

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:

`\begin{gathered} T-mg=m(v^2)/(r) \\ \\ T=m(v^2)/(r)+mg \end{gathered}`

Now, we can replace m = 27 kg, v = 3 m/s, r = 4 m, and g = 9.8 m/s² to get

`\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}`

Therefore, the answer is

A. 325.4 N