A heavy bird sits on a clothesline (which is basically just a horizontal string). Will the tension in the clothesline be greater if the line sags a lot (the bird is close to the ground) or if it sags very little? Explain your answer
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The tension will be greater if it sags very little.
Explanation: Tension is a force exerted by a rope, cable or string or any other object similar to them that are tightly pulled by opposite forces acting in both ends. When a heavy bird sits on a clothesline, the weight of the bird exerts an effort in the cable causing it to be deformed. The degree of deformation is dependent on how strong the force is. If there is a little sag, there will be more tension that is exerted since a force is needed to counter act the force brought by the weight of the heavy bird without deforming the clothesline so much. When there is a little sag, large vectors in the opposite sides are needed for a resultant force which is equal and opposite to the weight of the heavy bird.
The tension in the wire will be greater if the line sags little because the tension is how tight the string is, and the tighter the string is, the less chances it has of sagging when the bird is put on compared to a loose wire.
Tension is a scalar equal in magnitude to the force exerted by the ends of the string.
When the heavy bird sits on the clothesline, there is a downward force exerted on the spot where the bird sits. This is equal to F = m*g with m being the mass of the bird and g being the acceleration due to the gravitational force of attraction of the Earth.
Let x represent the angle made by the string and the horizontal at the point where the bird is sitting. If T is the tension in the string, 2*T*sin x is equal to the downward force F = m*g. As the strings sags down x increases. In the interval 0-90 degrees, sin x increases as x increases. As a result for the same value of m*g, the value of T would decrease if x were to increase.
As a result, the tension in the string would be lower if it sags a lot. As the tension in the string increases, the extent to which it sags decreases.
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