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Chris jumps off a bridge with a bungee cord (a heavy stretchable cord) tied around his ankle, Fig. $47 .$ He falls for 15 before the bungee cord begins to stretch. Chris's massis 75 $\mathrm{kg}$ and we assume the cord obeys Hooke's law, $F=-k x,$ with $k=50 \mathrm{N} / \mathrm{m}$ . If we neglect air resistance, estimate how far below the bridge Chris's foot will be before coming to a stop. Ignore the mass of the cord (not realistic,however) and treat Chris as a particle.

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$60 \mathrm{m}$

Physics 101 Mechanics

Chapter 8

Conservation of Energy

Work

Kinetic Energy

Potential Energy

Energy Conservation

Moment, Impulse, and Collisions

Stephany G.

October 23, 2022

hello i would like to asked....from where is the 59.4 value comes from?

Cornell University

Rutgers, The State University of New Jersey

University of Michigan - Ann Arbor

Simon Fraser University

Lectures

04:05

In physics, a conservative force is a force that is path-independent, meaning that the total work done along any path in the field is the same. In other words, the work is independent of the path taken. The only force considered in classical physics to be conservative is gravitation.

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In classical mechanics, impulse is the integral of a force, F, over the time interval, t, for which it acts. In the case of a constant force, the resulting change in momentum is equal to the force itself, and the impulse is the change in momentum divided by the time during which the force acts. Impulse applied to an object produces an equivalent force to that of the object's mass multiplied by its velocity. In an inertial reference frame, an object that has no net force on it will continue at a constant velocity forever. In classical mechanics, the change in an object's motion, due to a force applied, is called its acceleration. The SI unit of measure for impulse is the newton second.

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Okay, So for this bungee jump problem, we need to draw a sketch situation. So we re bungee jumper standing here with a rope attached to his feet and then a dislocation. Here he falls your distance. 0 15 meters. So we have a bungee jumper like this, and at this location, the card begins to stress. Still here, the court just fully extends about north stretch. And then finally, he comes to the lowest point of his jump right here, and the cord stretches by a distance off. Let's say X two some distance it stretches. And the total height office fall is H. So we neglect the air resistance. You have to estimate how far below the Chris below the bridge press foot would be before coming to a stop. So which means, writer dislocation. This is this foot. And this is the water surface. So the zero location, Uh, well, the first of all, only forces acting on the bunch of temporal gravity, you know, and diagnostic forces from the bungee cord. So jumpers, mechanical energy is conserved. So at location one, the jumper represents the bridge at this location, and the to it at disposition is in the bottom of the jump, the Louis point of a jump. So obviously, at this point, everyone is equal to zero and at this point also veto his equals. Zito and this location here via von is equals to etch and our dislocation here by to his equals to zero. But the stretch is equals to EJ minus 15. So we quit. Energies are these two locations even equals two. So the total energy and even half and even squared place mg y one bless half k x one squared that should be equals two half M. Vito squared Bless mg y two plus half G X two squared. No, we know that ve even equal zero. So therefore, this thing, this turn will cancel Why one equals zero. This turn will cancel on the left. You simply have all sorry. This term is not equals to zero here. So once again, everyone is equal to zero. Therefore, this terrible cancel. There is no stretch in the string in location one day for this tournament's cancel. So therefore we have the total energy on the left hand side is simply MGH On the right hand side, we have veto is equal zero Therefore, this term is going to cancel. And why? To a zero a zero this term is going to cancel. And the only energy on the underwriters The elastic credential, which is equal to half gay X to riches edge minus 15 squared. Now, in this, if you solve this equation, then you will get at squared minus 30 Place I do mg by K Edge plus 2 25 equals zero and you can convert this to the quadratic equation and substituting the mass. In this we'll get that squire minus 59.4 edge unless 225 equals zero. So the matter is given 75 kilograms. Solving this quadratic equation, you will get EJ as equals to 60 meters. They will get to roots. In this we'll get that one group has four and under Lord is bigger than four, which is what we should take. Um the bigger then the bigger value because the edge is greater than 15 meters because 15 meters is the is the UN stress length of string. So therefore we cannot select the lure hood. In this answer, we have to select the higher who So the answer is 60 meters

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