Question

A 100-n weight is hung at the middle of a 4-m long horizontal clothesline. If the middle of the clothesline sags by 1 m, what is the tension on each segment of the clothesline?

Answer 1

The tension on each segment of the clothesline is :  110 N

Given data :

mass of object = 100 n  = 10 kg

Horizontal distance of clothesline = 4 m

middle of clothesline sag s by : 1m

Determine the tension on each segment of clothesline

First step : calculate the horizontal angle made by the sagging

β = arctan ( 1 m / 2m )  ----- ( 1 )

  = arctan ( 0.5 )

  ≈ 26.57°

Note : Tension in th y axis ( Ty ) = Tsinβ

Therefore :

Tension on each segment can be calculated using the formula below

2Tsinβ - mg = 0

solve for T

T = mg / 2sinβ

  = ( 10 * 9.8 ) / 2 * sin 26.57°

  = 98 / 0.89

  = 110 N

Hence we can conclude that the tension on each segment of the clothesline is : 110 N

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