Bungee+Jumping

. This hits most of the concepts we will want students to cover in the bungee jumping action figure engineering activity. []

Great question! Let's look at this one part at a time. First, you asked about the forces on a bungee jumper.

The first force that the bungee jumper experiences is gravity, which pulls down on everything and makes the jumper fall. The gravitational force is almost exactly constant throughout the jump.

During the bungee jumper's fall, he or she also experiences a force due to air resistance. The faster the jumper is falling, the more the air resistance pushes back opposite to the direction of motion through the air.

The third force the jumper experiences is a spring force due to the bungee cord. The amount that the bungee cord pulls back on the jumper depends on how far the cord has been stretched, i.e. the farther the jumper has fallen, the more the cord pulls back on him or her. Below a certain height, the spring force of the bungee cord pulling up on the jumper exceeds the force of gravity pulling down. In that range, even ignoring the air resistance, the fall slows down, and then starts to reverse, so the jumper heads back up.

Now that you know about the forces, let's look at the work that is done on the jumper. Each little bit of work done on the jumper changes their kinetic energy, mv2/2, where m is their mass and v is their velocity. you calculate that work by multiplying the distance traveled times the component of the force in that direction. You can have negative work if the force and direction of motion are opposite to each other.

So now let's look at the first fall that the jumper makes. As the jumper falls down, gravity does positive work because the force of gravity points in the same direction that the jumper falls in. The spring force of the bungee cord, however, does negative work on the jumper because the jumper is falling down while the cord is pulling up. The third force, air resistance, also does negative work during the fall since it pushes upwards. As the jumper reverses direction and starts to spring back up, gravity does negative work because the gravitational force pulls down while the jumper is moving up. The spring force does positive work this time because it is in the same direction as the jumper's motion. However, air resistance still does negative work because now it pushes down on the jumper.

Now to finish off, let's look at the energy in this situation. There are three types of energy here: potential energy of gravity and in the stretched cord, kinetic energy of the jumper, and thermal (heat) energy of the air and other things. Gravitational potential energy depends on how high of the ground you are, e.g. if you hold a book above your head, that book has more potential energy than a book that is sitting on the ground. The potential energy of the bungee cord depends on how much the cord has been stretched, i.e. the bungee cord has more potential energy when it is stretched out than when it is slack. Kinetic energy depends on how fast you are moving, as we mentioned. One of the most important equations in physics is the work-energy equation.

If there weren't any air resistance, then we'd have a pretty simple result, because the potential + kinetic energy wouldn't change. At the top of the fall the jumper isn't moving, so the kinetic energy is zero. The gravitational potential energy there is large. At the bottom of the fall, again for an instant the jumper isn't moving and the kinetic energy is zero. There the gravitational potential energy has gone down, but the bungee cord potential energy has gone up so much that the total potential energy is back to the starting value. In between, the jumper has kinetic energy, so the gain of potential energy by the cord in that range isn't enough to make up for the loss of gravitational potential energy. Basically energy gets exchanged back and forth during the jump, and if air resistance were not present, the bungee jumper's total energy would remain constant and he or she would continue boinging up and down forever.

However, you know very well that this is not the case! So now let's take a look at air resistance and its effects on the bungee jumper. y. Air resistance is the main reason that the bungee jumper, on his or her way back up to the top, never quite reaches the place that he or she started the jump from. In fact, as the jumper bounces up and down, each time his or her maximum height gets less and less. This is similar to a ball that bounces lower and lower until it stops bouncing at all. This is because air resistance is working against the bungee jumper (and the bouncy ball) both on the way down and on the way up, i.e. it always does negative work and subtracts from the total energy of the bungee jumper. The jumper comes to rest right at the point where the cord pulls up just as much as gravity pulls down,

Does the energy just go away? Not really- air resistance, like all other friction forces, takes energy out of the big things you can see and dumps it into little jiggles of air molecules and similar small-scale stuff. In real life, there are some other types of friction here too. As the cord stretches and pulls back, there's some friction inside the cord itself. So even without air, the energy would gradually get dumped into heat.

. BELOW: Formula for the force on the body. Trauma due to bungee jumping. . . **THE BUNGEE JUMPING EXPERIENCE ** [] The topic of my exploration is bungee jumping, more specifically the math and science that allow bungee jumpers to jump from tall platforms and safely come within feet of hitting the ground. I chose this topic because I enjoy exhilarating amusement park rides such as roller coasters, drop zone and giant swings. I have yet to actually bungee jump and thought it wise to make sure I understood the concepts that keep me from plummeting to my death when I jump. Bungee jumping is interesting because it’s not just a person tied to a cord jumping off a bridge; there is actually math and physics involved in the process. From this math we can determine the height from which a person can bungee jump with a specific cord so that the person comes safely within feet of the ground. There is no guess work involved its all math. One needs a firm background in Algebra II, namely knowledge of equations and the use of variables and exponents, as well as a slight understanding of energy to understand the physics of bungee jumping.

Assuming you understand this math let us begin with the history of bungee jumping. Centuries ago bungee jumping first came into being on the Pentecost Island located in the South Pacific. Prior to WWII, the Vanuatuan natives were almost completely isolated. During the war the native’s practice of diving from a tower held only by a cord of vines was introduced to the world through a 1955 National Geographic article (“Bungee” 1). The article explained that according to legend, a domestic dispute was the cause for the first jump. An island native, Tamalie, mistreated his wife and she ran from him and climbed high into a banyan tree. Tamalie soon found her and climbed after her. As he was climbing the wife quickly tied lianas vines around her ankles so when Tamalie tried to grab her, she jumped out of the tree, and he jumped after her. The wife was smarter than Tamalie because he had no way to keep from hitting the ground while she experienced the physics of bungee jumping. Thus, the tradition began with the native men of the tribe promising to never let a woman get the best of them again and began performing these jumps annually off eighty foot towers to show their manliness. After more developments in science, this extreme sport was introduced in the United States in 1979 when four eccentric members of Oxford University Dangerous Sports Club jumped from the Golden Gate Bridge using latex cords. Hence, the Sport of bungee jumping became popular around the world (Frase 7).

Bungee jumping is defined as the sport of jumping, while attached to elastic chords, from a high platform. The cords allow the jumper to free fall toward the earth and then snatch the jumper back up before he hits the ground. Several falls and rebounds (oscillations) occur before the jump is completed. The jumper is connected to a bungee cord usually attached to a harness or the jumper’s ankles. This cord is then connected to a platform from which the jumper wishes to jump (Lam 1). In order to understand what is actually happening when a bungee jumper falls from a high platform and then recovers, we must look at a few of the different types of energy involved in the process. Energy is defined as the ability or capacity to do work (Curtin). As a jumper stands on a platform ready to jump he has gravitational potential energy (GPE). The energy is potential because it is not yet in use. It is stored energy ready to be used. Gravity (the force that pulls all objects in the universe toward one another) acts as the force that creates this energy. The equation for GPE = mgh. Where m is the mass of the object in kg (in this case the jumper), Galileo Galilei discovered that at a given location on the earth and in the absence of air resistance, all objects, regardless of mass, fall with the same constant acceleration (Giancoli 34). This constant is g. It is called the acceleration due to gravity and is approximately 9.8 m/s2 on earth. The variable h is the distance from the height of the platform to the ground (Curtin). As the jumper free falls the gravitational potential energy changes from potential energy to kinetic energy (KE) or energy in motion after the jumper has free fallen for the length of the cord elastic potential energy (EPE) comes into play (Lam 1). A bungee cord acts like a spring. If the cord is stretched past its natural unstretched position, it exerts a force that acts to restore the cord to its original position. This force is the elastic potential energy (Cooper 1). The cord begins to stretch when it passes the equilibrium point. The equilibrium point is a point where the cord lies from the top of the platform at its natural unstretched position (//see fig 1//). Energy transfers from kinetic energy into elastic potential energy. This same concept is exemplified when a person pulls a sling shot back to shoot a rock. At the point when the sling shot is pulled back there is elastic potential energy waiting to be used. When the person releases the pouch to let the rock come hurling out, the energy is transferred to kinetic energy. The equation for EPE = (1/2)KX2. The variable K (measured in N/m) is simply the spring constant. This differs with the various types of cords used in bungee jumping. The stiffer the cord, the larger the K. In the same equation, X stands for the elongation or stretch of the cord past the equilibrium point. Once the elastic cord passes its equilibrium point it begins to stretch. The distance it stretches is X and is measured in meters (//see fig 1//) (Cooper 1). As you can see, energy is transferred from GPE (gravitational potential energy) when the jumper is on the tower to KE (kinetic energy) when the jumper free falls and then to EPE (elastic potential energy) when the cord begins to stretch to its limit. After this stretch, the EPE then again turns back into KE. The point where this happens is the turn around point. It is where the jumper changes directions from going down and uses the potential energy in the cord to send him upward where he again gains more and more GPE until finally he stops once more and again changes directions and heads back down. This process repeats itself several times until finally all of the energy is used up by friction. In order not to complicate things, for our sake, we will assume that the law of conservation of energy holds true. The law states that if no dissipative forces are present, then the total amount of mechanical energy is constant. In other words, to perform our calculations we are going to assume that the GPE at the top equals the EPE at the bottom and that friction is not a factor (Giancoli 159).



A scientist named Robert Hook studied the physical characteristics of springs and rubber bands similar to the cord for a bungee jumper. He came up with a law that explained how the force exerted on your body by the cord is proportional to the distance of your body past the equilibrium point of the cord. This law can be expressed in the equation F=KX. Where the force is proportional to the stretch of the spring (K: spring constant; X: elongation of cord past equilibrium point) from this relationship. The K, or the spring constant, can be found for any cord. To find this value, the cord is attached to a known mass. The distance the cord stretches past the equilibrium point is used as X in the equation F=KX. Since the weight is not moving up or down, the forces are balanced. Therefore, the force of the cord equals the force of the weight pulling down. Thus an equation can be written (//see fig 1//). Since all of the variables are known except K, one can solve the value of the spring constant (Cooper 1). In bungee jumping, the cords are usually made of multiple strands of rubber that are bound tightly together and are cotton braided on the outside. They are usually 3/8 to 1 inch thick and have a breaking strength of up to 1000 pounds. (Frase 14). The energy equations previously explained can be put to use in solving problems involving a bungee jumper. Specifically, the question of this investigation is this: how do bungee jumpers determine the appropriate height of a platform to avoid hitting the ground. For explanation purposes, an example is best suited: A 10 meter cord with a spring constant of K=50 N/m is attached to a person weighing 75 kg. How high must the tower be so that the person comes within 2 meters of hitting the ground? To solve this problem we apply our knowledge of energy. The person jumping has only gravitational potential energy (GPE) while standing at the top of the tower (//see fig 2//). After he jumps, this energy is transformed to elastic potential energy (EPE) at the bottom. Assuming the law of conservation of energy, these two equations can be set equal to each other since no energy is lost or gained in the process -- only transferred. With the given information we can solve for h (the height from the tower to the ground) and add 2 to this number to get the height the jumper must jump from to come within 2 meters of hitting the ground (//see fig 2)// (Curtin).

**Physiology of Bungee Jumping** **[]** A bungee jump can be separated on three different stages: Free fall, Body deceleration, and Upward movement.
 * First Stage - Free fall .** During this stage, all jump stress hormones, like beta-endorphin, growth hormone, prolactin, testosterone,and adrenalin, are supposed to be released. Several evidences obtained from monitoring jumps, show that it really occurs and it could explain the feelings of exhilaration and well being that often occurs and last for some days after a single jump. The theory that prolonged rises in brain neurotransmitter concentration can occur is being studied.
 * Second Stage - Body deceleration.** A sudden body deceleration occurs because the elastic property of the cord ( Hook’s law- F=KX) . The intensity of deceleration depends on the kind of cord used and the altitude of the jump. The more intense decelaration the more is the risk of injuries. At this stage an increasing head ward fluid shift take place, consequently the hydrostatic pressure in the blood vessels of eye becomes dangerously high. Because the head-down position a sudden rise in intrathoracic pressure also occurs and it is one of the major damage event.
 * Third Stage- Upward movement.** It is characterized by an upward movement in a head-down position. It is responsible for a further increasing in intrathoracic and head blood vessels pressures. According to some aviation studies, forces exceeding -3g (it is frequently reached during a bungee jump) are able to cause hemorrhages. Furthermore, an extreme bradycardia can occurs leading to syncope. The mechanism is supposed to be mediated for baroreceptors when a sudden and substantial headward shift of blood volume occurs.


 * Injuries**
 * Head -** The head injuries have resulted in extensive damage to the eyes involving the retina and others structures such as fovea, macula, and internal limiting membrane, as well as the vitreous body and conjunctiva. In the most of cases, a temporary visual impairment is the result of these injuries. Reported injuries include nasal and temporal bilateral subconjunctival hemorrhages, subconjunctival chemosis (infection), and bilateral multiple parafoveal dot and blot hemorrhages.
 * Trunk -** The trunk injuries can be divided in three distinct categories : shoulder, back, and spine injuries. The shoulder injuries are dislocations and soft tissues damage as occurs in back injuries.
 * Lower extremities-** The peroneal (fibular) nerve injury is frequently involved in bungee jumping. This damage leads to a cutaneous anesthesia of the lateral aspect of the leg, foot, and ankle, as well as marked weakness in dorsiflection and eversion of the foot. These are the classical signs and symptoms of peroneal nerve palsy. The excessive traction on the nerve is the probable reason for the palsy.