When you think about it, the pole vault is quite interesting. There is a bar 4 to 5 meters high that you want to clear. Jumping won’t cut it. Your only option is to run as fast as you can and use a long pole to vault over the bar.
Historically, the pole vault was first used to get over canals and marshes. It was simply a matter of maximizing your horizontal distance. In the mid-1800s, some bright guy thought he’d see how high he might get pole vaulting. The modern pole vault was, according to Wikipedia, born with its first proper competition in Germany in 1950. The original poles were stiff, but over time flexible poles of fiberglass and, later, carbon fiber allowed athletes to achieve ever-greater heights. The current outdoor record, set by Sergey Bubka in 1985, stands at an amazing 6.14 meters.
So, how does this work? This is a great example of the work-energy principle. In case you don’t recall your high school physics, the work-energy principle essentially says the work done on a system is equal to the change in energy for that system.
For the case of a pole vaulter, I can pick the Earth, the pole and the vaulter all as the system. This means that there is no work done and I can write the following for the change in energy:
Here, K is the kinetic energy and the other two terms are for the gravitational potential and spring potential energy. Let me go ahead and write the definitions of these energies, just to be thorough.
Let’s put this to use. The question to look at is: How important is the running part of a pole vault? When dealing with the work-energy principle, you must always choose two positions to examine. In this case, let me start with position No. 1 right at the end of the vaulter’s run and position No. 2 when the vaulter is at the highest point. Here is a diagram:
Notice that I skipped the whole “the pole bends” part. If I assume there is no energy lost during this time (no work done on the system), then that part doesn’t matter. What does matter is that at position No. 1, the person is running and has kinetic energy. Then, at point No. 2, the person isn’t moving (at least not too much), so there isn’t any kinetic energy.
For the gravitational potential energy, I can let the potential energy be zero at position No. 1. This means that the potential energy at position No. 2 just depends on the increase in height of the center of mass of the vaulter (as seen in the diagram). And what about the spring potential energy? At both position 1 and 2, the pole is not bent. This means that there is no spring energy stored in either position. With this, I can re-write the work energy equation as:
One nice thing is that the mass cancels. Let me now use this to find out how fast you must run to get to reach Bubka’s outdoor record of 6.14 meters. First, the height is the height of the bar, not the change in height for the center of mass. I will use a change in height of maybe 5 meters. In this case, I can solve for the needed velocity beforehand and I get:
Just to get a feel for this speed, 9.9 m/s is about 22 mph. Yes. That is seriously fast. That is why this calculation is mostly wrong. Yes, wrong. There are two things missing. The vaulter can add extra energy to the system in two ways. First, the vaulter doesn’t just run but instead runs and jumps. If a person just stands still and jumps, they could probably increase the height of his or her center of mass by at least 0.5 meters. The other extra energy comes from right before position 2. The vaulter isn’t an inanimate object. Instead, he or she can push on the pole to gain extra height. Both of these would mean that the vaulter wouldn’t have to run as fast.
But what about the pole? Isn’t the pole important? Of course you can’t pole vault without a pole. To see the effect of the pole, consider the energy kinetic energy during the run. If the runner were moving vertically, this motion would carry the vaulter to the height as described previously. However, the vaulter is running horizontally. So how do you take this kinetic energy associated with the run and change it into energy needed to move vertically upward? The answer: You need to cheat. Cheat energy, that is.
This is where the pole comes into play. As the runner plants the pole in the ground, the pole flexes. The flex in the pole is almost exactly like the compression of a slinky. The more the pole bends, the greater the stored elastic potential energy. Where does the energy to bend this pole come from? It comes from the kinetic energy of the vaulter. As the horizontal motion stops, the pole then releases this stored elastic energy as it pushes the vaulter upward. So, in short the pole takes horizontal kinetic energy and stores it before using it to increase the gravitational potential energy of the vaulter.
by: Rhett Allain