- #1
sunniexdayzz
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Homework Statement
Consider a bungee cord of unstretched length L0 = 43 m. When the cord is stretched to L > L0 it behaves like a spring and its tension follows the Hooke’s law T = k(L − L0). But unlike a spring, the cord folds instead of becoming compressed when the distance between its ends is less than the unstretched length: For L < L0 the cord has zero tension and zero elastic energy. To test the cord’s reliability, one end is tied to a high bridge (height H = 147 m above the surface of a river) and the other end is tied to a steel ball of weight mg = 120 kg×9.8 m/s2. The ball is dropped off the bridge with zero initial speed. Fortunately, the cord works and the ball stops in the air 14 m above the water — and then the cord pulls it back up. Calculate the cord’s ‘spring’ constant k. For simplicity, neglects the cord’s own weight and inertia as well as the air drag on the ball and the cord. Answer in units of N/m.
Homework Equations
F=ma
T=k(L-L0)
gravity = 9.8m/s^2
The Attempt at a Solution
I tried to figure out the Tension by using f=ma
I assumed that acceleration at the bottom of the rope was 0 .. but now thinking about it i don't think that's true. so then if T is tension and G is the mass x gravity then T + G = ma
then i would plug in T for hooke's law and solve for k.
I guess my biggest problem is figuring out what T is.