It’s your birthday, and to celebrate you’re going to make your first bungee jump. You stand on a bridge above a raging river and attach a -long bungee cord to your harness. A bungee cord, for practical purposes, is just a long spring, and this cord has a spring constant of . Assume that your mass is . After a long hesitation, you dive off the bridge. How far are you above the water when the cord reaches its maximum elongation?
The distance between you and water when the bungee cord is at maximum elongation.
Height of the bridge,
Length of bungee cord
The spring constant of the cord
The potential energy of the cord:
The elastic energy of the cord,
By conservation of energy, equate potential energy and elastic energy.
Distance of the cord
The distance of the cord is below the water.
The elastic energy stored in your tendons can contribute up to 35, of your energy needs when running. Sports scientists find that (on average) the knee extensor tendons in sprinters stretch 41 mm while those of nonathletes stretch only 33 mm. The spring constant of the tendon is the same for both groups, 33 N/mm. What is the difference in maximum stored energy between the sprinters and the nonathletes?
In a hydroelectric dam, water falls 25 m and then spins a turbine to generate electricity.
a. What is ∆UG of 1.0 kg of water?
b. Suppose the dam is 80% efficient at converting the water’s potential energy to electrical energy. How many kilograms of water must pass through the turbines each second to generate 50 MW of electricity? This is a typical value for a small hydroelectric dam.
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