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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]

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 chil class=

Respuesta :

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

Also centripetal force,

[tex]\begin{gathered} F=T-mg \\ =1040-800 \\ =240\text{ N} \end{gathered}[/tex]

Mass of the swing can be obtained using the weight

[tex]\begin{gathered} mg=800 \\ m=80\text{ kg} \end{gathered}[/tex]

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

Centripetal force can also be written as

[tex]F=ma[/tex]

Here, a is the Centripetal acceleration.

Thus, centripetal acceleration is

[tex]\begin{gathered} a=\frac{F}{m} \\ =\frac{240}{80} \\ =3m/s^2 \end{gathered}[/tex]

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

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