IMathAS-libretexts

This block has a a mass $\displaystyle {m}$ and is being held up by two ropes. The first rope ( $\displaystyle {T}$ ₁) is at angle of θ₁. The second rope ( $\displaystyle {T}$ ₂) is at angle of θ₂. Because they are at unequal angles, they have different tensions acting on the point where all three ropes converge. The first step to solving this problem is breaking the forces into components and deciding which equation they will go in. Assuming that up is the $\displaystyle +{y}$ direction and right is the $\displaystyle +{x}$ direction, match the following force components to the coordinate direction.

$\displaystyle {m}{g}$
$\displaystyle {T}_{{1}}{{\cos{\theta}}_{{1}}}$
$\displaystyle {T}_{{1}}{{\sin{\theta}}_{{1}}}$
$\displaystyle {T}_{{2}}{{\cos{\theta}}_{{2}}}$
$\displaystyle {T}_{{2}}{{\sin{\theta}}_{{2}}}$

$\displaystyle +{x}$
$\displaystyle -{x}$
$\displaystyle +{y}$
$\displaystyle -{y}$

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