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Difficult

Balanced Swing

APPH12-IZKAWR

A boy and a girl are sitting on a porch swing that is $1.5 \text{ meters}$ long and weighs $200 \text{ Newtons}$. There are two chains connected at the two ends of the swing.

The boy weighs $600 \text{ Newtons}$ and sits at a distance equal to one third of the length of the swing from the left side of the swing. The girl weighs $400 \text{ Newtons}$ and sits at a distance equal to one third of the length of the swing from the right side of the swing.

What is the tension in the chain on the left, ${ T }_{ A }$ and the tension in the chain on the right, ${ T }_{ B }$ when the swing is in equilibrium?

A

${ T }_{ A}=733\text{ N}$
${ T }_{ B }=467\text{ N}$

B

${ T }_{ A}=667\text{ N}$
${ T }_{ B }=333\text{ N}$

C

${ T }_{ A}=767\text{ N}$
${ T }_{ B }=433\text{ N}$

D

${ T }_{ A}=633\text{ N}$
${ T }_{ B }=567\text{ N}$