Question

In a tug of war, the members of team A pulls with a force of 100N, 115N, 125N . Team B pulls with the force of 105N, 128N, 107N. what is the net force? ​

Answer 1

net force is 0

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Answer 2

The force applied by members of team A be

$F_1 = + 100N$

$F_2 = + 115N$

$F_3= + 125N$

$\underbrace{⠀⠀⠀⠀⠀⠀⠀ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: }⠀⠀⠀⠀⠀⠀⠀⠀⠀$

$\purple{\boxed{\frak{ + ve \: sign \: is \: taken \: as \: we \: considered \: these \: forces \: are \: pulling \: the \: rope \: along \: + ve \: x \: axis}}}$

If the force applied by members of team B be

$F_4 = - 105N$

$F _ 5= - 128N$

$F _6= - 107N$

$\underbrace{ ⠀⠀⠀⠀⠀⠀⠀ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: ⠀}$

$\pink{\boxed{\tt{ -ve \: sign \: is \: taken \: as \: these \: are \: acting \: by \: the \: members \: of \: team \: b \: in \: the \: direction \: opposite \: to \: the \: direction \: of \: team \: a}}}$

$\tt\blue{net \: force \: F = }\tt\orange{F _1 + F _2 +F _3 + F _4 + F _ 5+ F _6}$

$\tt\orange{ = + 100N + 115N + 125N + ( - 105N) + ( - 128N) + ( - 107N) }$

$\tt\orange{ = ( 100 + 115 + 125 - 105 - 128 - 107)N}$

$\tt\orange{ = (340 - 340)N}$

$\tt\orange{ = 0N}$

$\tt\therefore{the \: net \: force \: is \: zero }$

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