A flexible chain of weight W hangs between two fixed points, A and B, at the same level, as shown in Fig. Find (a) the force exerted by the chain on each endpoint and (b) the tension in the chain at the lowest point.

The flexible chain that has a weight W hangs between two fixed points A and B which are at the same horizontal level. The inclination of the chain with the horizontal at both the points of support is theta . The weight of the chain is a downward acting force at the center of mass of the chain which lies at the mid point. The tension in the chain is the same throughout the chain and is a force that equals the net force acting on the chain. If the tension is F, this can be divided into components in the horizontal direction and the vertical direction. The force in the horizontal direction is F*cos theta this components cancels out. The vertical component is equal to 2*F*sin theta and this is equal to the weight of the chain W. 2*F*sin theta = W => F = W/(2*sin theta) => F = (W/2)*cosec theta The tension in the chain is equal to (W/2)*cosec theta

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W/2 sim theta

W/2 sin theta

Tension at middle point will be W cot theta /2

Tension at end points will be W closed theta /2

Tension at end points will be W cosec theta /2