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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.
Question
d) How will it (that the backpack disappears at the lowest point) affect that vertical swing movement? Justify the answer briefly.
e) From the moment the backpack falls off, it will take a certain time Tp before P reaches its equilibrium position. Find Tp.
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