Transfer of Energy When Jumping off the Golden Gate Bridge

Introduction

 Fig. 1: Graph of suicide jumps off the Golden Gate Bridge per year. [3] (Source: Wikimedia Commons)

Last year 46 people jumped off the Golden Gate Bridge, falling to their death. Since the bridge has opened, more than 1600 people have fallen to this same fate. During that same span 26 people have jumped and actually survived, making the survival rate a measly 1.6%. [1] An obvious connection between transferring energy and jumping off a bridge has to do with movement, because movement is kinetic energy. [2] I want to evaluate how fast someone is going when they hit the water. When evaluating the movement from jumping off the Golden Gate Bridge, we most focus on equations for the gravitational potential energy (GPE) and kinetic energy (KE):

 UGPE = m × g × h EKE = 1/2 mv2

Situation

To plug in numerical values for each variable we must set up the situation. When modeling a question for physics we must make basic assumptions that help us get to an answer. Basic assumptions in this scenario include assuming that air resistance is negligible. We make this assumption despite knowing that the air resistance would decrease a jumpers velocity due to drag. A jumper will continue to experience this decrease in speed until they reach their terminal velocity which is around 53 m/s. We choose to leave out this important factor for simplicity. Another assumption could include that we are calculating their GPE from the person's mass relative to their center of mass. Lastly we are assuming that he is starting from rest (he's not moving when he starts). The GPE of the person is at its max when the person is at rest at the top; the KE is at 0. [2] However when the person hits the water, the KE is at its maximum and GPE is 0. Because of the full transfer of energy, we know that the two maximums of GPE and KE are the same value. Now that we know that these two equations equal each other, we can fill in the variables in the equation that we do know in order to figure out the velocity (the speed we are traveling). For GPE, we will use an average weight of a male for mass, 89 kg. 9.8m/s2 represents the g in the equation, with the height of the bridge being 67 meters. This results in the GPE equaling 58,437 joules. Using this we can set 1/2 mv2 to 58,427 joules because all the potential energy has been converted to kinetic energy. To solve for v we multiply both sides by two and divide by m, then take the square root. This comes out to approximately 36 meters per second.

Conclusion

We cannot technically calculate the absolute gravitation potential energy, what we are more focused on is the change in gravitational potential energy between the point of when the person jumps off the bridge and when they hit the water. After calculating the velocity of the person as they enter the water, it is easy to see why jumping from this bridge has been so lethal. To put it into more relative terms, 36 meters per second is like hitting the water going 80 miles per hour. Because we must take gravitational acceleration into account, it would take about 3.7 seconds for a person of this mass to hit the water after jumping of the Golden Gate Bridge. The off chance that a person survives likely has to do with how enter the water. A blow to the neck being the most deadly. [1]

© Tomas Hilliard. The author grants permission to copy, distribute and display this work in unaltered form, with attribution to the author, for noncommercial purposes only. All other rights, including commercial rights, are reserved to the author.

References

[1] E. N. Lorenz, "Available Potential Energy and the Maintenance of the General Circulation," Tellus 7, 157 (1955).

[2] M. Blaustein and A. Fleming, "Suicide From the Golden Gate Bridge," Am. J. Psychiat. 166, 1111 (2009).

[3] E. Guthmann, "Beauty and an Easy Route to Death Have Long Made the Golden Gate Bridge a Magnet for Suicides," San Francisco Chronicle, 30 Oct 05.