A 1.84 kg school bag hangs in the middle of a clothesline, causing it to sag by an angle θ = 3.50°. Find the tension in the clothesline. (Ans. 148N)



Given:

Mass of bag = w = 1.84 N
Angle θ = 3.50° 

To Find:

Tension = T = ?

Solution:

After resolving the tensions (forces) into its components. we get horizontal components for both Tensions are T cos θ and T cos θ and Vertical components are T sin θ and T cos θ (both directed upwards).

Now according to the first condition of equilibrium:

Along X-axis:

Σ Fx = 0
T cos θ - T cos θ = 0

Along Y-axis:

Σ Fy = 0
T sin θ + T sin θ - W = 0            [W  downwards]

or

2T sin θ  =  W

2T sin θ  =  mg         [W = mg]

by putting values

2T sin 3.50° = 1.84 kg x 9.8 ms⁻² 

2T x 0.061  = 1.84 N 

T x 0.122  = 18.05 N   

T  = `frac {18.05 N}{0.122}`

T  = 147.95

T = 184 N   --------------Ans.

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