A body weighing 8 N is supported by two cables whose voltages T1 and T2 form angles of 60 ° and 30 ° with the ceiling. How much are these tensions worth? Choose the correct option. Select one: a. 4N and 7N b. 5N and 7N c. 4N and 10N

a. 4N and 7N

Explanation:

Draw a free body diagram.

Sum of the forces in the x direction:

∑F = ma

T₂ cos 30° − T₁ cos 60° = 0

T₂ cos 30° = T₁ cos 60°

T₂ (½√3) = T₁ (½)

T₁ = T₂ √3

Sum of the forces in the y direction:

∑F = ma

T₂ sin 30° + T₁ sin 60° − mg = 0

T₂ sin 30° + (T₂ √3) sin 60° − mg = 0

½ T₂ + 1.5 T₂ − mg = 0

2 T₂ = mg

T₂ = 4 N

T₁ = 4√3 N

T₁ ≈ 7 N

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