How does center of gravity affect an athlete's jumping ability?

[ravsterphysics]

Homework Statement

I'm having a hard time visualising how center of gravity can affect height of an object.

Right now I'm looking at an example of an athlete bending their knees to shift their centre of gravity so they can jump higher, and how if during takeoff they push their arms upward they can jump even higher.

Can someone explain how this works? I've sat through a few youtube videos but I'm still confused.

Homework Equations

The Attempt at a Solution

 

[Cutter Ketch]

I can see how that would be confusing. There are several things going on. First is the distance over which the athlete pushes. The muscles can only generate so much force and so only so much acceleration. If you can't increase the force any more what can you change to achieve more vertical velocity? If the athlete can push for a longer distance they accelerate for more time and reach a higher vertical velocity. So they start with the center of gravity as low as they can (as low as they can still generate a significant force that is) and they push until their center of gravity is as high as they can get it. Accelerating that whole time and distance they achieve the highest vertical velocity.

Force times time is impulse. That is the change in momentum and since the mass doesn't change goes directly to velocity. Force times distance is energy and is also connected directly to velocity.

The hands up increases the height of the center of gravity as I have said. However getting to the highest point does more than just increase the pushing time. As soon as the feet leave the ground you are done pushing. Your center of gravity will fly in a parabolic arc until you touch back down. You want that starting point to be as high as possible. Raising your arms and stretching your toes to raise your COM another inch is like jumping from a platform that is that much above the ground.

The final important thing is which muscles do the jumping. Going from a crouched position to stretched out as high as you can reach involves a lot of muscles. All of those movements pushed the center of mass higher. All of those movements accelerated the body upward, and so much more muscular energy goes into the jump than if you jumped with... say ... your calf muscles alone

Hope that helps

 

[ravsterphysics]

I can see how that would be confusing. There are several things going on. First is the distance over which the athlete pushes. The muscles can only generate so much force and so only so much acceleration. If you can't increase the force any more what can you change to achieve more vertical velocity? If the athlete can push for a longer distance they accelerate for more time and reach a higher vertical velocity. So they start with the center of gravity as low as they can (as low as they can still generate a significant force that is) and they push until their center of gravity is as high as they can get it. Accelerating that whole time and distance they achieve the highest vertical velocity.

Force times time is impulse. That is the change in momentum and since the mass doesn't change goes directly to velocity. Force times distance is energy and is also connected directly to velocity.

The hands up increases the height of the center of gravity as I have said. However getting to the highest point does more than just increase the pushing time. As soon as the feet leave the ground you are done pushing. Your center of gravity will fly in a parabolic arc until you touch back down. You want that starting point to be as high as possible. Raising your arms and stretching your toes to raise your COM another inch is like jumping from a platform that is that much above the ground.

The final important thing is which muscles do the jumping. Going from a crouched position to stretched out as high as you can reach involves a lot of muscles. All of those movements pushed the center of mass higher. All of those movements accelerated the body upward, and so much more muscular energy goes into the jump than if you jumped with... say ... your calf muscles alone

Hope that helps

Thanks for the detailed explanation.

Okay but why does moving their centre of gravity to a lower point allow them to push off with more force?

And why does centre of gravity need to high for them to reach a higher point? If you look at this video (2 mins 42 seconds) you can see that the jumper attains a higher jump but their centre of gravity is lower than them:

 

[haruspex]

why does moving their centre of gravity to a lower point allow them to push off with more force?

It does not allow them to push off with greater force; it allows the force to be applied for longer, so reaching a higher take-off speed.

why does centre of gravity need to high for them to reach a higher point? If you look at this video (2 mins 42 seconds) you can see that the jumper attains a higher jump but their centre of gravity is lower than them:

Good technique will make the height cleared as high as possible for a given height of mass centre, but for a given technique the higher the mass centre the higher the bar cleared.