For the chain in the previous problem, find the force necessary so that the center of the chain is no more than 0.500 m lower than the ends of the chain.

Previous Problem

If the two ends of a completely flexible chain (one that requires no force to bend it) are suspended at the same height near the surface of the earth, the curve representing the shape of the chain is called a catenary. It can be shown that the catenary is represented by

y = a cosh (x/a),

where a = T /gρ and where ρ is the mass per unit length, g is the acceleration due to gravity, and T is the tension force on the chain. The variable x is equal to zero at the center of the chain. Construct a graph of this function such that the distance between the two points of support is 10.0 m, the mass per unit length is 0.500 kg m⁻¹, and the tension force is 50.0 N.