# Slacklining

A slackline is stretched between two trees at a distance, $$d = 10\,\text{m}$$, so that a tensioning force, $$F_0 = 5000 \,\text{N}$$, is applied on the empty rope. A man then balances in the middle of the rope and exerts a weight force, $$F_g = 750 \,\text{N}$$, onto the slackline. What is the vertical deflection, $$h$$, of the rope?

Details and Assumptions: The rope is made of an elastic material and obeys Hooke's law $$F = K \frac{l - l_0}{l_0},$$ where $$F$$ is the force along the rope, $$l_0$$ is the initial length, $$l$$ is the stretched length of the rope, and $$K = 150\text{ kN}$$ is the force constant.

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