A load of 10.0 N is suspended from a clothesline. This distorts the line so that it makes an angle of 15° with the horizontal at each end. Find the tension in the clothesline.

[Ans: 19.3N]

Given: 

Load = `\vec {W}` = 10.0 N
Angle with X-axis = θ = 15⁰

To Find:

Tension in the cloth line = T = ?


Solution:

This numerical problem is illustrated in the given below figure.

Here we have resolved the Tension in the clothes wire into x and y - components as shown in the figure. 

To solve this problem, we have to satisfy the 1st condition of equilibrium. i.e. to prove  Σ Fx = 0 and Σ Fx = 0 

for Σ Fx = 0
we have two horizontal forces (X-axis) 
T cos 15⁰ along the positive x-axis (X) and
-T cos 15⁰ along the negative x-axis (X')

so, 

Σ Fx = T cos 15⁰ + (-T cos 15⁰) =  T cos 15⁰ - T cos 15⁰) = 0


for Σ Fy = 0
we have three vertical forces (Y-axis), T sin 15⁰ (left side) and T sin 15⁰ (right side) are upward forces along the positive y-axis (y), and the load w = 10 N is a downward force along the negative y-axis (y')

so, 

Σ Fy = T sin 15⁰ + T sin 15⁰ - W = 0

putting values

2 T sin 15⁰  - 10 = 0

2 T sin 15⁰  = 10 

or

T sin 15⁰  = 5

T  = `\frac {5}{ sin 15⁰ }`

T  = `\frac {5}{ 0.2588 }`

T  = 19.3 N --------Ans


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Numerical Problem 2.15
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List of 11th Physics Numerical Problems of Chapter - 2
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