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
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).
Summary: The bungee jump scenario involves diving off a bridge 120 m above a river with a 32-m-long bungee cord attached. The cord has a spring constant of 45 N/m, and the mass of the person jumping is 77 kg.
Explanation: To calculate the maximum extension of the bungee cord, we need to use Hooke's Law, which states that the force exerted by a spring is proportional to its displacement. The equation is F = -kx, where F is the force, k is the spring constant, and x is the displacement.
First, we need to find the gravitational force acting on the person, which is given by the equation Fg = mg, where m is the mass and g is the acceleration due to gravity (approximately 9.8 m/s^2). So, Fg = 77 kg * 9.8 m/s^2 = 754.6 N.
Next, we can find the maximum extension of the bungee cord. We know that the maximum force exerted by the cord is equal to the weight of the person, so Fmax = 754.6 N. Plugging this into Hooke's Law, we get -kx = 754.6 N, where k is 45 N/m. Solving for x, we find x = -754.6 N / (-45 N/m) = 16.77 m.
Therefore, the maximum extension of the bungee cord during the jump is 16.77 m. This means that the person will be stopped by the bungee cord when they have fallen 120 m - 16.77 m = 103.23 m above the river.