Answer to Question #148173 in Classical Mechanics for Lisa Kip

Question #148173
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
1
Expert's answer
2020-12-03T10:20:45-0500

"\\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



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