Kevin A. Kirby said:
Potential and Kinetic Energy Exchanges in Bouncing Balls and in Running
Running is a relatively energy-efficient locomotor activity due to the ability of the muscles and tendons within our feet and lower extremity to store and then release elastic strain energy during the running gait cycle.
The potential and kinetic energy exchange of running is mechanically analogous to the potential and kinetic energy exchange of a bouncing ball.
If a ball is resting quietly on the edge of a table (see illustration below), it has no kinetic energy (KE). KE becomes larger when the velocity is larger
However, at this point, with the ball at rest above the ground, the ball still has potential energy (PE).
PE is larger when the height of the ball above the ground is larger.
In other words, when the ball is resting quietly on the table, it has 0% KE and 100% PE.
As the ball rolls off the end of the table, gravity starts to accelerate the ball towards the ground and it starts to lose vertical height from the ground.
The increase in downward velocity of the ball toward the ground causes an increase in KE, but the loss in vertical height from the ground causes a decrease in PE in the ball.
At the instant the ball strikes the ground, it is at its greatest velocity so that, at this instant in time, the KE is at its maximum.
However, since the ball now is touching the ground, and thus has no vertical height from the ground, it has no PE.
Therefore, at the instant the ball strikes the ground, it has 100% KE and 0% PE.
The downward momentum of the ball (momentum = velocity x mass) will cause the ball to compress, making the ball temporarily flatter, after it impacts the ground.
This deformation of the ball stores elastic strain energy withing the internal structure (i.e. molecular structure) of the ball.
Elastic strain energy is a type of PE.
Therefore, when the ball has completely stopped its downward movement and the ball has been fully compressed by its downward momentum, it will now have 0% KE (due to the ball's velocity being zero) and 100% PE (due to the storage of elastic strain energy within the compressed ball).
The fully compressed ball will now rapidly recoil back to its original shape which accelerates the ball upward away from the ground.
As the ball rapidly accelerates upward and just starts to leave the ground with a large upward vertical velocity, the KE is 100%.
However, the PE is 0% at this instant in time since the elastic strain energy has been completely released when the ball returned to its uncompressed state and since the ball now has no vertical distance from the ground.
As the ball accelerates vertically upward, it starts to lose KE due to gravity decelerating its upward flight.
At the same time, the movement of the ball upwards allows the ball to gain PE due to its increasing height above the ground.
At the apex of its flight upward, the ball now is at its maximum vertical height so that it has 100% PE.
However, since the ball has just transitioned from a upwards to a downwards flight, and has zero velocity at this instant in time, it has 0% KE.
The ball will continue bouncing up and down without any additional input of energy until the energy lost from internal friction within the ball and the energy lost due to air resistance during the ball's flights causes the ball to rest quietly on the ground.
At the instant the ball stops bouncing and is resting quietly on the ground, the ball's velocity is zero (KE=0) and the ball's vertical height is zero (PE=0).
Much like the bouncing ball, a runner use potential and kinetic energy exchange to improve the mechanical efficiency of running.
The runner will raise their center of mass (CoM) to a peak at the middle of the double-float phase of running where their PE is at 100% but their vertical KE is 0%.
Gravity will then accelerate their CoM downward until footstrike where downward velocity is the greatest and PE is at 0% and KE is 100%.
As the muscles and tendons of the lower extremity are then stretched and store elastic strain
energy during the first half of the support phase of running which the CoM is being decelerated by the lower extremity, the PE within the lower extremity increases to a maximum and the KE drops again to zero at the middle of the support phase of running.
Then as the muscles and tendons within the lower extremity release their stored elastic strain energy, the runner's CoM is accelerated upwards and forwards, until the runner again reaches the apex of their vertical ascent during the middle of the double float phase of running again, where their PE will
be at 100% and the KE will be at 0%.
Without this continual exchange of potential and kinetic energy, a ball would not continue to bounce when dropped from a height and the runner could not run efficiently or for long periods of time.
Understanding this exchange of potential and kinetic energy in both bouncing balls and in running is one of the keys to fully understanding the biomechanics of running which is critical information that will allow the sports clinician to most effectively treat their runner patients.
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