A pole-vaulter runs toward the launch point with horizontal momentum. Where does the vertical momentum come from as the athlete vaults over the crossbar?
Pole vaulters have three things going that help them clear a very high bar.
(1) The angular momentum about the place there the pole is stuck into the ground is preserved, which helps to push the vaulter upward. In order for this to happen, the pole pushes the vaulter upward.
(2) Flexible poles, which have been allowed since about 1960, store kinetic energy of the running vaulter as potential energy, which is released when the pole is vertical and straightens out again.
(3) When the pole is vertical, a skilled vaulter will push his or her center of mass upward, becoming upside down to gain an extra 3 or 4 feet of height, bending the waist as it passes over the bar.
As the pole-vaulter runs towards the launch point with horizontal momentum, the vertical momentum during the vault comes from the conversion of the horizontal momentum into vertical momentum. This conversion is achieved through certain techniques and movements performed by the pole-vaulter.
Once the pole-vaulter plants the pole into the ground and takes off, they use their horizontal momentum to drive the pole down and flex it, storing elastic potential energy. As the pole recoils and extends, it transfers energy back to the athlete. The pole-vaulter then uses this stored energy to launch themselves upwards, transferring their horizontal momentum into vertical momentum.
During the vault, the pole-vaulter generates force against the pole through their body movements, such as pushing off the ground with their feet and swinging their legs upwards. This force helps propel them upwards, allowing them to gain vertical momentum and clear the crossbar successfully.
The vertical momentum of the pole-vaulter comes from the conversion of their horizontal momentum into vertical momentum during the vault.
To understand how this happens, let's break it down step by step:
1. Approach: The pole-vaulter starts by running towards the launch point with a certain amount of horizontal momentum. This horizontal momentum is determined by the velocity of the vaulter, which is a combination of their speed and direction.
2. Takeoff: As the vaulter reaches the launch point, they plant the pole in the ground and push off it, transferring some of their horizontal momentum into the pole. This action results in a decrease in the vaulter's horizontal momentum but does not affect their vertical momentum significantly yet.
3. Ascent: The pole starts bending and recoiling, propelling the vaulter into the air. As the pole straightens, it transfers the stored energy into the vaulter, causing them to gain vertical momentum, propelling them upward over the crossbar. This conversion of potential energy (stored in the bent pole) to kinetic energy (upward motion of the vaulter) leads to an increase in vertical momentum.
4. Crossbar Clearance: The vaulter continues to gain height until they clear the crossbar. At this point, the pole-vaulter's vertical momentum is at its maximum, achieved through the conversion of their initial horizontal momentum into vertical momentum during the ascent.
5. Descent: After clearing the bar, the vaulter begins to descend due to the force of gravity. During the descent, the vaulter's vertical momentum gradually decreases until they land safely on the landing mat. This decrease occurs because their initial horizontal momentum has been mostly converted into vertical momentum during the vault.
In summary, the vertical momentum of the pole-vaulter is generated through the conversion of their initial horizontal momentum into vertical momentum during the vault, facilitated by the bending and recoiling of the pole.