# Mechanics problem - Newtons laws - resultant force

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I have this mechanics problem. Please help me solve it.

Rory, Aurora and Raoul are three lions fi ghting over a piece of meat of mass 12
kg.
Each lion exerts a horizontal pull. Rory pulls with a force of 800 N.
Aurora, who is 120degrees to Rory's right, exerts a force of 400 N.
Raoul is 140 degrees to Rory's left.
The meat accelerates in Rory's direction.
(a) Find the force which Raoul is exerting.

Thank you in advance.

• Mechanics problem - Newtons laws - resultant force - ,

Let F-Raoul be the force exerted by Raoul.
Consider the direction perpendicular to Rory's direction,
There is no nett force in that direction as there is no movement along it.
F-Raoul Cos(40º) = 400 N * Cos(60º) ------> F-Raoul = 261 N
Nett force in Rory's direction = 800 N - 261 N * Sin(40º) - 400 N * Sin(60º).
You just apply F = m*a to find the acceleration.

• Mechanics problem - Newtons laws - resultant force - ,

In the case of resolving the force perpendicular to Rory's direction, isnt it suppose to be F-Raoul cos(50º) = 400 cos(30º) ?

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