Question

A rope at a 45° angle from the roof and a rope at a 55° angle from the roof is holding a pizza that weighs 380 N you need to find the tension of both ropes. It is at equilibrium

Answer 1

$\vec{T}= \vec{T_1}+\vec{T_2}$

$|\vec{T}| =|\vec{F_p}|$

$\vec{T_1}= \vec{T}*cos(\alpha)$

$\vec{T_2}= \vec{T}*cos(\beta)$

$|\vec{T_1}|= |\vec{F_p}*cos(\alpha)|=380*cos45^0\approx268.7$

$|\vec{T_2}|= |\vec{F_p}*cos(\beta)|=380*cos55^0\approx218$

$\text{where }\vec{T}\text{ total reaction force}$

$\vec{F_p}\text{ pizza that weighs}$

$\vec{T_1},\vec{T_2},\alpha,\beta - \text{rope tension forces and roof corners}$

Answer: 268.7N and 218 N - rope tension