Bungee jumping: Kinematics, energy and period of oscillation
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Your adventurous friend Lola goes bungee jumping. She leaps from a bridge that is 100 m above a river. Her bungee cord has an unstretched length of 55 m and a spring constant k=750 N/m. Lola has a mass of 45kg
1. How fast is she falling when she just starts to stretch the cord? How long does it take for Lola to reach this point?
2. Lola stretches the bungee cord and it brings her to a stop. She then bounces back up again. What type(s) of mechanical energy does the system (Lola and the bungee cord) have just before she jumps? (I.e. gravitational PE, elastic PE, kinetic energy, etc.) What type(s) of energy does the system have at the instant she comes to rest at her lowest point?
3. What is her height above the river at her lowest point? (Hint: use energy for this, assume no energy is lost, and remember that the energy stored in a stretched bungee cord (or spring) is (1/2)k(delta x)^2, where (delta x) is the amount of stretch)
4. What would be the period of her oscillation if we assume the bungee cord acts like a perfect spring?
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