Level 1: A Rope Holds Twice Your Weight: Is a Swing From Level Safe?
Start the swing from sixty degrees.
A person swings down from rest on a rope, starting with the rope at 60° to the vertical. At the lowest point, the tension in the rope is:
Starting at 60° to the vertical, the person drops through a height L(1 − cos 60°) = L/2 to the lowest point, so energy conservation gives v² = gL there.
The tension is twice the weight, exactly the rope's limit in the Level 1 question, so it would only just survive. In general the tension at the bottom is mg(3 − 2 cos θ₀) for a start at angle θ₀ to the vertical.
Every Level 2 starts from a quick question, Level 1, and changes one thing. Seeing what that change does is the skill JEE Main tests. Try it here, free and with no signup, then read the worked answer.
