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A horizontal clothesline is tied between 2 poles, 10 meters apart.
When a mass of 5 kilograms is tied to the middle of the clothesline, it sags a distance of 4 meters.

What is the magnitude of the tension on the ends of the clothesline?

Respuesta :

okpalawalter8

The magnitude of the tension on the ends of the clothesline  is  mathematically given as

T= 47.6194N

What is the magnitude of the tension on the ends of the clothesline?

Generally, the equation for AB^2 is  mathematically given as

AB² = AQ² +BQ²

Therefore

AB²=5²+32

AB² = 25+9

AB² = 34

AB=√34

sin ∅ = ав AB

Sin∅ = 3 √34

Let T1 and T₂ be tension  in AB and BC respectively

The horizontal component of tension. T1 cos∅ = T₂cos ∅

T₁ = T₂

The vertical component of tension

T1 sin∅. + T₂ sin ∅ = mg

Tsin∅+ Tsin∅ = mg

T = mg/2sin∅

T=5*9.82/ 2 sin ∅

[tex]T=\frac{5*9.8}{2*3/\sqrt{34}}[/tex]

T= 47.6194N

In conclusion, the magnitude of the tension

T= 47.6194N

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