The remarkable physics of a powerful vault
It’s rather hard to believe that the world record in the pole vault is over 20 feet. That’s twice the height of the “high dive” at your local pool. Expertise in the pole vault requires speed, skill, strength, and kamikaze-style fearlessness. It also requires a method to convert the kinetic energy of the approach into the maximum possible gravitational potential energy. That’s where the pole comes in.
Pole vaulting without a pole is called the high jump, and although the world record in that event is an astonishing 8 feet or so, somewhere in the process of jumping, as we transfer horizontal motion into vertical motion, we lose some of the energy of the approach. Also, high jumpers can’t approach the bar at a full sprint, because biomechanically you can’t generate the maximum vertical push-off while running at top speed.
However, notice those extremely flexible poles in the video. As long as they don’t break, it’s that elasticity which makes it possible to transfer the kinetic energy of the approach into elastic potential energy in the pole. The elastic energy is then reconverted to kinetic energy (with the motion redirected upward), and that is in turn transformed to gravitational potential energy at the top of the vault.
According to the principle of conservation of energy, in an isolated system the total energy of the system is constant. In the case of a pole vault, we might express the energy transformations as follows:
KEapproach = PEelastic = KEvault = PEgravitational
Skipping the intermediate steps, we can see that the initial kinetic energy on the approach should equal the final gravitational potential energy at the top.
If we apply a quick conservation-of-energy calculation to the vault, we get a pretty interesting result. Recall from physics class that
KE = ½ mv2 where m is the mass of an object in motion and v is its velocity, and PEgravity = mgh where g is the acceleration due to gravity (9.8 m/s2 on Earth) and h is the height of the object.
Now if we estimate a maximum approach velocity of 10 m/s for the vaulter, and assuming we can convert all of the kinetic energy of the approach into gravitational potential energy at the top we get:
½ mv2 = mgh
Solving for h we get a maximum height of approximately 5.1 m. Even assuming 100 percent conversion of energy, that’s still about a meter short of the actual world record vault!
So where does the extra energy come from? It’s the same source that provides the energy for the sprint down the runway — chemical potential energy stored in chemical bonds in the muscle cells of your body. We can therefore rewrite our equation as:
KEapproach + PEinternal/chemical = PEgravitational
When vaulters plant the pole they must unleash some stored internal chemical energy and add it into the system, giving the extra “oomph” necessary to clear that ridiculously high bar.
And that’s why pole vaulting is such hungry work, my friends!
Adam Weiner is the author of Don’t Try This at Home! The Physics of Hollywood Movies.