Difficulty understanding Centre of Gravity

[trew]

Homework Statement

Difficulty understanding Centre of Gravity

Relevant Equations

n/a

Hey,

This isn't a homework question I need help with but more of a concept I can't seem to grasp.

I understand that Centre of Gravity is: the point on a body where all the weight can be considered to act.

And I understand how to find this point on different types of bodies.

However, this sort of question has me stumped:

Part (a) is straightforward enough, but part (b) has me confused.

I can see that the centre of gravity is lower on the fosbury flop than the straddle jump but I don't get why this matters.

I've looked at videos that go over the physics of the fosbury flop and they talk about how the centre of gravity is lower than the beam that the person is trying to jump over thus making it easier.

BUT I just don't get how this works. So what if the centre of gravity is lower, why does this allow the person to jump higher?

I'm trying to find other real life examples of centre of gravity to get some sort of context for this concept but I'm struggling.

Can anyone break it down for me? What am I missing here?

 

[Orodruin]

The center of gravity will undergo approximately parabolic motion determined by how the jumper manages to get off the ground. Given the same parabola, the center of mass will undergo the same motion regardless of how you turn your body so to clear a bar that is as high as possible, your lowest point should be as high as possible relative to the center of mass when passing the bar.

 

[hmmm27]

Chain Fountain

There was a homework question on here a little while ago, involving a long long train going over a hill.

It might look like a very large amount of energy would be needed but, in reality, once the front of the train crests the peak, it starts to pull the rest of the train over the hill, behind it.

 

[trew]

The center of gravity will undergo approximately parabolic motion determined by how the jumper manages to get off the ground. Given the same parabola, the center of mass will undergo the same motion regardless of how you turn your body so to clear a bar that is as high as possible, your lowest point should be as high as possible relative to the center of mass when passing the bar.

I appreciate your post but this is what I don't understand.

What does it mean to have centre of gravity high or low? I get that a 4x4 car has a high centre of gravity so it's easier to topple over, but I understand this intuitively and based on real world experiences and nothing else.

But what does centre of gravity mean and why does it suddenly mean I can jump over a beam easier if the centre of gravity point is beneath the horizontal beam?

For example, if I sit down or bend my knees to get lower, I intuitively understand that I'm going to be harder to topple over. I've seen this in MMA fights and other sports. But how and why does this work?

Also, if I stand up straight and jump, but then I bend my knees and jump again, I'll jump higher compared to the first try. I know this has something to do with centre of gravity but again, I don't get how this works.

 

[PeroK]

I appreciate your post but this is what I don't understand.

What does it mean to have centre of gravity high or low? I get that a 4x4 car has a high centre of gravity so it's easier to topple over, but I understand this intuitively and based on real world experiences and nothing else.

But what does centre of gravity mean and why does it suddenly mean I can jump over a beam easier if the centre of gravity point is beneath the horizontal beam?

For example, if I sit down or bend my knees to get lower, I intuitively understand that I'm going to be harder to topple over. I've seen this in MMA fights and other sports. But how and why does this work?

Also, if I stand up straight and jump, but then I bend my knees and jump again, I'll jump higher compared to the first try. I know this has something to do with centre of gravity but again, I don't get how this works.

The basic idea of the high jump is that you have to leave the ground with as much upward speed as possible. This determines how high your centre of gravity will go. But, depending on your body position, you may or may not get over a bar.

Suppose my centre of gravity is $1m$ off the ground and I leave the ground at $\sqrt{20} m/s$. Then I can get another $1m$ off the ground.

If I just jump straight at the bar then my feet will knock it off, even if the bar is only $1m$ about the ground.

I could pull my feet up and hurdle the bar, that might be a bit better.

Better, is twisting so that I am roughly horizontal as I go over the bar. In that way I might be able to clear nearly 2m. But, if you look at the guy in the straddle, even if his centre of gravity is $2m$ off the ground, he's struggling to clear $1.90m$.

So, what else could you do. It looks like $2m$ is the absolute max that you can clear if you can only get your centre of gravity $2m$ off the ground.

But, what if, you get you head, shoulders and upper body over the bar, arching your back. Then, once your back is clear, you flip your legs up to get them clear of the bar. You might have cleared the bar without your centre of gravity ever having been higher than the bar.

In that way, it's possible than you could clear up to $2.10m$, if you get the timing right and are flexible enough, even if you can only "jump" $2m$.

That's the point of the flop: to utilise the flexibility of the human body. You don't actually jump any higher, in the sense of the speed you leave the ground or the max height of your centre of gravity. Instead, you manoeuvre your way over the bar.

 

[haruspex]

why does this allow the person to jump higher?

That's the thing - the person is not jumping higher, just smarter.

Consider a hollow cylinder with longitudinal strip missing from the side. You roll this towards a horizontal bar which is almost as high off the ground as the top of the cylinder. When you get to the bar, friction with the ground being small, you may be able to rotate the cylinder so that the bar goes into the gap in the cylinder. Now you turn the cylinder on the spot nearly one full turn. When you roll the cylinder forward again, the bar exits the cylinder through the gap.
It cost you almost no energy to get the cylinder past the bar because its centre of gravity hardly rose.

 

[trew]

TEXT.

That's the thing - the person is not jumping higher, just smarter.

TEXT.

Thanks for the explanations. I think I'm beginning to see the bigger picture.

What would help is I can get my understanding of centre of gravity right.

You can see here that the persons centre of gravity is low so he is harder to push over.

And every resource (so far) that I've come across states this. BUT, no resource is telling me why this is. Why does the centre of gravity being lower help stabilise a person? Does it have something to do with Newton's laws?

At this point I think I'm not understanding why any of this is going on.

 

[PeroK]

Thanks for the explanations. I think I'm beginning to see the bigger picture.

What would help is I can get my understanding of centre of gravity right.

View attachment 242302

You can see here that the persons centre of gravity is low so he is harder to push over.

And every resource (so far) that I've come across states this. BUT, no resource is telling me why this is. Why does the centre of gravity being lower help stabilise a person? Does it have something to do with Newton's laws?

At this point I think I'm not understanding why any of this is going on.

It's all to do with Newton's laws, as applied in classical mechanics. The low centre of gravity is not the whole story. In this case it's the squat position. Why is a table harder to topple than a bookcase?

You need to be able to analyse forces, torques and moments. In the simplest case, a bookcase will fall over as soon as its centre of gravity is no longer above the base. That's hard to do for a table.

The man in the picture is the same: it's difficult to get his centre of gravity beyond his back feet. It's much easier to do if he's standing with his feet together.

 

[hurreechunder]

Thanks for the explanations. I think I'm beginning to see the bigger picture.

What would help is I can get my understanding of centre of gravity right.

View attachment 242302

You can see here that the persons centre of gravity is low so he is harder to push over.

And every resource (so far) that I've come across states this. BUT, no resource is telling me why this is. Why does the centre of gravity being lower help stabilise a person? Does it have something to do with Newton's laws?

At this point I think I'm not understanding why any of this is going on.

Specifically for the case of toppling over someone squatting low vs high: toppling happens when the centre of gravity goes outside the base. Why? Well, as long as it is inside the base, gravity tries to turn it the other way and back to its sitting position. When the CG goes outside the base, gravity just topples it over. Mathematically, this happens because the angle between the CG and the point of contact of the object changes from less than 90 deg to more than 90 deg, and that changes the direction of the torque given by mg cos theta. The lower the CG the more you’ll need to tilt the object to make the CG fall outside the base, and hence the more difficult it is. Conversely, with a high CG, a slight tilt can make the CG fall outside the base and cause the object to topple over

 

[CWatters]

I can see that the centre of gravity is lower on the fosbury flop than the straddle jump..

I don't think that is necessarily correct.

It takes energy to raise the CoG from it's height when standing to some maximum height during the jump (m*g*Δh). A jumper can only produce a limited amount of energy so no matter which technique he uses both will probably raise the CoG to about the same height.

The difference is that with the flop the part directly above the bar can be higher than the CoG.

 

[hurreechunder]

I don't think that is necessarily correct.

It takes energy to raise the CoG from it's height when standing to some maximum height during the jump (m*g*Δh). A jumper can only produce a limited amount of energy so no matter which technique he uses both will probably raise the CoG to about the same height.

The difference is that with the flop the part directly above the bar can be higher than the CoG.

The point is that with the CoG raised to the same height, the Fobsbury flop can clear a higher bar, which is what wins in high jump. This video from the 1980 Moscow Olympics shows both jumps. The straddle looks a lot harder because the CG needs to go above the bar and hence higher: