A 30.0-kg girl in a swing is pushed to one side and held at rest by a horizontal force / vec{F} F ⃗ so that the swing ropes are 30.0^/circ30.0 ∘ with respect to the vertical. Calculate the tension in each of the two ropes supporting the swing under these conditions.

169.74 N

Explanation:

Given,

Mass of the girl = 30 Kg

angle of the rope with vertical, θ = 30°

equating the vertical component of the tension

vertical component of the tension is equal to the weight of the girl.

T cos θ = m g

T cos 30° = 30 x 9.8

T = 339.48 N

Tension on the two ropes is equal to 339.48 N

Tension in each of the rope = T/2

= 339.48/2 = 169.74 N

Hence, the tension in each of the rope is equal to 169.74 N