Question

A child that weighs 800 N swings on a swingset. When the child is at the lowest point in the arc, the total tension in the swing chains is 1040 N. What is the child's centripetal acceleration?[Use g = 10 m/s2]

Answer 1

Given that the downward weight, mg = 800 N and tension in the swing is, T = 1040 N.

Also centripetal force,

`\begin{gathered} F=T-mg \\ =1040-800 \\ =240\text{ N} \end{gathered}`

Mass of the swing can be obtained using the weight

`\begin{gathered} mg=800 \\ m=80\text{ kg} \end{gathered}`

Here, g = 10 m/s^2 is the acceleration due to gravity.

Centripetal force can also be written as

`F=ma`

Here, a is the Centripetal acceleration.

Thus, centripetal acceleration is

`\begin{gathered} a=(F)/(m) \\ =(240)/(80) \\ =3m/s^2 \end{gathered}`

Hence the child's centripetal acceleration is 3 m/s^2