A m = 2.45 kg object hangs in equilibrium at the end of a rope (taken as massless) while a wind pushes the object with a F W = 18.9 N horizontal force. Find the magnitude of the tension in the rope and the rope's angle from the vertical. The acceleration due to gravity is g = 9.81 m/s2.

Question

Amanda

Physics

7 September, 23:43

A m = 2.45 kg object hangs in equilibrium at the end of a rope (taken as massless) while a wind pushes the object with a F W = 18.9 N horizontal force. Find the magnitude of the tension in the rope and the rope's angle from the vertical. The acceleration due to gravity is g = 9.81 m/s2.

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Gunner Chang · Answer 1

Tension on the rope = 30N

Angle from the vertical = 38.79°

Explanation:

The vertical force on the rope is given by:

F v = mg

Given: m = 2.45kg

Vertical force Fv = 2.45 * 9.8 = 23.52N

Tension on the rope, T = Sqrt (18.9^2 + 23.52^2)

T = sqrt (357.21 + 553.19)

T = sqrt (910.4)

T = 30N

Vertical angle, theta = Tan^-1 (18.9/23.52)

Theta = Tan^-1 (0.8036)

Theta = 38.79°