It's your birthday, and to celebrate you're going to make your first bungee jump. You stand on a bridge 120 m above a raging river and attach a 32-m-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 45 N/m. Assume that your mass is 77 kg. After a long hesitation, you dive off the bridge.GENERATE THE ANSWER IN 150 WORDS IT WILL BE DIVIDED INTO TWO PARAGRAPHS THE FIRST PARA WILL BE THE SUMMARY OF THE ANSWER in 2 lines, AND SECOND PARA WILL BE THE EXPLANATION OF THE ANSWER SHOW CALCULATION

Question

GPT 3.5 · Answer

Summary: Based on the given information, the maximum distance the bungee cord will stretch is calculated using Hooke's Law and the force of gravity. The results indicate that the bungee cord will reach a maximum extension of 0.63 m.

Explanation: In order to calculate the maximum distance the bungee cord will stretch, we need to use Hooke's Law. Hooke's Law states that the force exerted by a spring is proportional to the displacement or extension of the spring. The equation for Hooke's Law is F = -kx, where F is the force, k is the spring constant, and x is the displacement.

First, we need to calculate the force exerted by the bungee cord at its maximum extension. The force can be determined using the mass of the person and the acceleration due to gravity. The formula for force is F = mg, where m is the mass and g is the acceleration due to gravity. Plugging in the values, we get F = 77 kg * 9.8 m/s^2 = 754.6 N.

Next, we can use Hooke's Law to calculate the maximum displacement or extension of the bungee cord. Rearranging the equation, we have x = -F/k. Plugging in the values, we get x = - 754.6 N / 45 N/m = -16.77 m. Since displacement cannot be negative, we take the absolute value, resulting in x = 16.77 m.

However, since the bungee cord is only 32 m long, it will stop stretching and start to compress before reaching the calculated maximum extension. Therefore, the bungee cord will only stretch up to its length, resulting in a maximum extension of 0.63 m (32 m - 16.77 m).