This physics project analyzed video footage of a pole vaulter to determine if mechanical energy is conserved. Theoretical calculations showed that the vaulter's initial kinetic energy should equal their potential energy at the peak, requiring an initial velocity of 7.5 m/s. Experimental analysis of video footage found the vaulter's actual initial kinetic energy and velocity were lower. This suggests energy is added from an outside source, likely the chemical energy from the vaulter's muscles. Therefore, mechanical energy cannot be determined to be conserved due to this additional non-mechanical energy input.

1. Physics 211
Anran Chen
Cole Christensen
Margaux Pugh
Ty Sterk
Physics of Pole Vaulting
Introduction
Our project is an analysis of the sport of pole vaulting. We analyzed video footage (see
references for link to video) of a pole vaulter in order to determine whether mechanical energy is
conserved during a pole vault event. We analyzed the video using Logger Pro analysis software
to determine the displacement of the pole vaulter. Additionally, we used the acquired data to
determine his velocity in the y­direction (vertical), his potential energy based on how high he
goes, and determined whether kinetic energy at the beginning is equal to potential energy at the
highest point. First, we calculated a theoretical pole vault in which we showed that initial kinetic
energy should equal the gravitational potential energy at the highest point of the pole vault. We
calculated the experimental pole vault shown in the video in which we found the unknown
horizontal velocity of the runner by calculating the necessary kinetic energy to transfer into the
pole, back into the pole vaulter, and “spring” him up to the measured y­distance shown in the
video, what we found surprised us.
Theoretical Calculations
The potential energy at the top of the pole vault, according to the law of conservation, should be
equal to the total mechanical energy. To find this theoretical value, we determined the height of
the pole vaulter as he went over the pole and his horizontal velocity at the top of the vault. The

2. mass of the pole vaulter was estimated based on the weight recommendations for a thirteen
foot pole, which was used in this video.
Eq. 1: U = ­mgy
U = ­77kg (­9.8 m/s^2) (2.8 m)
U = 2100 J
Eq. 2: K = ½ mv^2
K = ½ (77 kg) (1.354 m/s)^2
K = 71 J
The total mechanical energy is the combination of the potential and kinetic energy at a single
point. If mechanical energy of the system is conserved, then the kinetic energy of the pole

3. vaulter running up for the vault would theoretically be 2171 J because there is no potential
energy before the vault.
Eq. 3: K = ½ mv^2
2171 J = ½ (77 kg) v^2
v = 7.5 m/s
The theoretical velocity he must have run to have a initial kinetic energy of 2171 J is 7.5 m/s.
We compare this theoretical initial kinetic energy and velocity to our calculations from the video
data.
Experimental Analysis
The video we used for analysis uses a still camera focused just on the vault and the jump, not
the run up. We ultimately calculated his initial kinetic energy through a backward calculation
since his initial velocity running up could not be determined by the video. First, we calculated the
spring constant of the pole, assuming that the pole functions similarly to a typical spring. As he
is ascending when the pole is expanding, there are two forces acting on him, the gravitational
force and the force upward applied by the pole. The acceleration “a” in eq. 4 is his average
vertical acceleration as the pole is extending found from the video analysis. And the distance “x”
is the displacement that the 13 foot pole was bent.

4.
Eq. 4: F aΣ = m
F​pole​ – F​grav​ = ma
k(x) ­ mg = ma
k(1.66 m) ­ 77 kg (­9.8 m/s^2) = 77 kg (1.096 m/s^2)
k = ­403.7 N/m
Using the calculated spring constant of the pole, we calculated the force needed to compress
the pole a displacement of 1.66 m.
Eq. 5: F​app​ = ­k(x)
F​app​ = ­(­403.7 N/m) (1.66 m)
F​app​ = 670 N

5. Using the force the pole vaulter must have used to compress the pole in Eq. 5, we calculated
his acceleration.
Eq. 6: F​app​ = ma
670 N = 77 kg (a)
a = 8.7 m/s^2
From his acceleration, we then found his horizontal velocity as he was running up to compress
the pole. The change in time ( ) is the amount of time it took for the pole to go from straight totΔ
being bent the furthest.
Eq. 7: v/Δta = Δ
.7 m/s v/0.6 s8 2 = Δ
v .22 m/sΔ = 5
Finally, we solved for his initial kinetic energy by using the velocity found above in Eq. 7:
Eq. 8: /2 mvK = 1 2
/2 (77 kg)(5.22)K = 1 2
049 JK = 1
The initial velocity of the pole vaulter before he planted the pole was found to be 5.22 m/s and
his initial kinetic energy was then found to be 1049 J using this method of backwards calculation
(Eq. 4­8).
Discussion
From the previous calculations, we found that the initial velocity and kinetic energy of the pole
vaulter running (Eq. 7 and 8) is significantly lower than the theoretical values (Eq. 1­3) under the
assumption of energy conservation. There is potential for some errors in our calculations and a

6. good amount of uncertainty due to certain assumptions that we made. For example, we
assumed the pole acts like a typical spring but it very well might not exhibit the exact same
spring behavior. Additionally, there is some uncertainty related to the method by which we
calculated all of our figures since there are implicit errors related to video software. However, we
would also imply that the pole vaulter somehow adds energy to the pole vault from some source
other than the measurable kinetic energy through merely running up to the point where he sticks
the pole in the ground. It is very plausible for the pole vaulter to add energy to the motion as he
compresses the pole. It is not a far stretch to say that the average athlete could add 100 N of
force with each arm at least the distance of each arm. This would account for roughly 500 J of
work done by each arm and could easily be the source of our unaccounted for “extra” energy.
Therefore, we are unable to determine whether or not mechanical energy is conserved
throughout a pole vault because their is an added source of outside energy. Upon researching
the potential cause of our added energy, we stumbled across an article in ​Popular Science
magazine, “​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” (1). We conjecture that the extra energy comes from the pole
vaulter himself and the chemical reactions that occur in his body.
Conclusion
We found in our theoretical calculations in section one that mechanical energy should be
conserved throughout the motion of a pole vault. The initial kinetic energy of the run­up to the
plant should be equal to the gravitational potential energy of the pole vaulter at the top of his
motion. However, in our experimental analysis of an actual pole vaulting video we found that

7. initial kinetic energy of the pole vaulter was significantly lower than the gravitational potential
energy at the highest point of the motion. This implies that energy is added to the pole vaulter
system from some outside source. As such, we were unable to determine whether or not
mechanical energy was conserved throughout the pole vault because energy was brought into
the system from some outside, non­mechanical (likely chemical) energy source.
References
1. Weiner, Adam. "Pole Power." ​Popular Science​. Popular Science, 2 Jan. 2009. Web. 25
Nov. 2014. <​http://www.popsci.com/scitech/article/2009­01/pole­power​>.
2. https://www.youtube.com/watch?v=PZUy_zpdemo