A person is standing with a backpack on a bridge and is going to do a bungee jump. He is very scared and takes small steps until he becomes unstable and falls forward. (see figure) We make a simplified model of the situation where we think thatthe person has an even mass distribution and the width xp = 30 cm The backpack also has an even mass distribution and the width xs = 20 cm. Assume that all movement (in the fall) occurs only vertically. We also assume that the elastic acts as an ideal feather. Ignore air resistance. The elastic has a length (equilibrium length / rest length) of 15 m andthe spring stiffness is 250 N / m. The person who jumps has a mass of 80 kg and the backpack has a mass of 25 kg, while the elastic is massless. Consider the person with the backpack as a rigid body Q. Question a) What is the position x0 to Q as he becomes unstable and falls off the bridge? In the following, we consider the situation after the person has fallen from the bridge. Now assume that Q is a one-point mass attached to the end of the elastic. Question b) Calculate the equilibrium position for the motion (ie where Q could in principle be suspended) in relation to the bridge. c) What is the lowest height the bridge can have so that Q does not hit the ground? At the lowest point in the swinging motion, the person suddenly loses the backpack. The person (now the backpack) should be considered as a point mass P.
A person is standing with a backpack on a bridge and is going to do a bungee jump. He is very scared and takes small steps until he becomes unstable and falls forward. (see figure)
We make a simplified model of the situation where we think thatthe person has an even mass distribution and the width xp = 30 cm The backpack also has an even mass distribution and the width xs = 20 cm.
Assume that all movement (in the fall) occurs only vertically. We also assume that the elastic acts as an ideal feather. Ignore air resistance.
The elastic has a length (equilibrium length / rest length) of 15 m andthe spring stiffness is 250 N / m. The person who jumps has a mass of 80 kg and the backpack has a mass of 25 kg, while the elastic is massless.
Consider the person with the backpack as a rigid body Q.
Question
- a) What is the position x0 to Q as he becomes unstable and falls off the bridge?
In the following, we consider the situation after the person has fallen from the bridge. Now assume that Q is a one-point mass attached to the end of the elastic.
Question
- b) Calculate the equilibrium position for the motion (ie where Q could in principle be suspended) in relation to the bridge.
- c) What is the lowest height the bridge can have so that Q does not hit the ground?
At the lowest point in the swinging motion, the person suddenly loses the backpack. The person (now the backpack) should be considered as a point mass P.
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