Question

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.

Answer 1

Tension on the rope = 30N

Angle from the vertical = 38.79°

Step-by-step 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°