How Does a Pole Vaulter's Center of Gravity Affect Maximum Jump Height?

In summary, the pole vaulter with a mass of 70kg and a top speed of 9.5 m/s is able to clear a bar height of 5.4m. Using conservation of energy, the maximum height the vaulter should be able to clear is 5.8m when taking into account the vaulter's center of gravity point being 90cm above their feet. The energy conversions that take place during the jump involve kinetic energy transforming into energy to bend the pole, which then converts into gravitational potential energy to lift the vaulter to a higher height. The addition of the center of gravity point allows for a more accurate prediction of the vaulter's maximum height clearance.
  • #1
clipperdude21
49
0
1. A 70kg pole vaulter runs with a top speed of 9.5 m/s. During the jump the pole is highly curved then straigtens out. The vaulter is able to clear a bar height of 5.4m
a) Using conservation of energy, determine the maximum height the vaulter should be able to clear. The vaulters center of gravity point is 90cm above his feet.
b) Discuss the energy conversions that take place.




2. K=.5mv^2, Ug=mgh



3. (a) .5mv^2=mgh. I got h is equal to 4.9m but I added the center of gravity point to make it 5.8 m. Is this right? why do we add the COG point?
(b) Kinetic energy transforms to energy into the bending the pole, the pole then converts the energy into gravitational potential energy by raising you a height H.



Thanks!
 
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  • #2
clipperdude21 said:
why do we add the COG point?

Because the energy equations allow you to predict how far the running vaulter, given a perfect vaulting technique, has the energy to lift their COG.

Taking the vaulter as a point (in which case how can their COG be above their feet?!), adding the height of the COG gives you an indication of the height the vaulter should be able to clear.

Taking the vaulter as having size and an adjustable shape, the vaulter can adjust their shape and thus put their COG below the part of their body that is passing over the bar. This allows the vaulter to clear higher than predicted by converting KE to GPE and adding the height of COG above ground when running. The question does not give any data allowing you to compute this third term of the height the vaulter should be able to clear.
 
Last edited:
  • #3


I appreciate your interest in applying the principle of conservation of energy to this scenario. The conservation of energy states that energy cannot be created or destroyed, but can only be transformed from one form to another. In the case of the pole vaulter, the initial kinetic energy from running is transformed into potential energy as the vaulter jumps over the bar.

To determine the maximum height the vaulter should be able to clear using conservation of energy, we can use the equation E=K+U, where E is the total energy, K is kinetic energy, and U is potential energy. At the maximum height, all of the initial kinetic energy will be converted to potential energy. Therefore, we can set the initial kinetic energy (calculated using K=.5mv^2) equal to the potential energy at the maximum height (calculated using Ug=mgh).

(a) By setting these two equations equal, we can solve for h, the maximum height the vaulter can clear. I also added the center of gravity point to the height because the vaulter's entire body needs to clear the bar, not just their feet. Therefore, the center of gravity point is used as a reference point for the height. Your calculation of 5.8m seems correct.

(b) The energy conversions that take place during the pole vault can be broken down into three stages: the initial running stage, the bending of the pole, and the jump over the bar. In the initial running stage, the vaulter's kinetic energy is provided by their own muscle power. As the pole is highly curved and then straightens out, the bending of the pole converts some of the vaulter's kinetic energy into elastic potential energy stored in the pole. Finally, as the vaulter jumps over the bar, the stored elastic potential energy is converted into gravitational potential energy, allowing the vaulter to clear the height of the bar. Overall, the conservation of energy principle allows us to understand and predict the maximum height a pole vaulter can clear, and the energy transformations that occur during the jump.
 

Related to How Does a Pole Vaulter's Center of Gravity Affect Maximum Jump Height?

1. What is the law of conservation of energy?

The law of conservation of energy states that energy cannot be created or destroyed, but it can be transformed from one form to another. This means that the total amount of energy in a closed system remains constant over time.

2. Why is conservation of energy important?

Conservation of energy is important because it is a fundamental law of physics that helps us understand and predict the behavior of systems. It also plays a crucial role in sustainable development and reducing our impact on the environment.

3. What are some examples of conservation of energy in everyday life?

Examples of conservation of energy in everyday life include turning off lights when leaving a room, using public transportation or carpooling to reduce fuel consumption, and using energy-efficient appliances and light bulbs.

4. How does the conservation of energy relate to renewable energy sources?

The conservation of energy is closely related to renewable energy sources, as these sources harness energy from natural processes such as sunlight, wind, and water without depleting finite resources. By using renewable energy sources, we can reduce our reliance on non-renewable sources and help conserve energy for future generations.

5. Can energy be completely conserved?

According to the law of conservation of energy, energy cannot be created or destroyed, but it can be transformed. Therefore, energy can be conserved in the sense that the total amount of energy in a closed system remains constant, but it is constantly changing form.

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