Simple Conservation of energy question

[Derek1997]

Homework Statement

Pole-vaulting is a fantastic example of energy being converted from one form to another. A pole- vaulter 1.7 m tall runs at 30 km/h (8.4 m/s) with her pole before starting her jump. The kinetic energy she generates is converted into elastic potential energy of the pole bending.This is then returned to the jumper as gravitational potential energy. Assume that her centre of mass is 55% of her height:
1)-Show that the height achieved of 4.6 m is close that that predicted by simple conservation of energy equations
2)- Discuss why this calculation is not exact - including consideration of the fact that the women’s pole vault world record is over 5 meters and that it’s not possible to run faster than 30 km/h with a
Thanks

Homework Equations

The Attempt at a Solution

Well, I got 3.6h for my first question i did KE=P and solved for h. Although I am not sure it said 4.6 and I got 3.6. Also for second part I say because since world record is 5m and not possible run more than 30, this athelte did run 30km and acheived lower than world record? thanks

 

[BvU]

Hello Derek, ,

Culture at PF is that you show your work in detail and we'll ask questions and give hints etcetera. (It doesn't help you if we do the exercise for you )

You got 3.6 m (meter, I hope, not hours ) starting from where ?

 

[TomHart]

I got 3.6 m too for the increase of her height.

 

[Derek1997]

Hello Derek, ,

Culture at PF is that you show your work in detail and we'll ask questions and give hints etcetera. (It doesn't help you if we do the exercise for you )

You got 3.6 m (meter, I hope, not hours ) starting from where ?

Hi, So i got 3.6 as height using the equation but I hope I am in a right track, so it says height of achieved is close to 4.6m which I don't get it, but for explaining second part I said it's because even tho he/she ran for 30km/h achieved fairly low height (3.6m)

 

[jbriggs444]

So i got 3.6 as height using the equation

Using what equation? As BvU has suggested, you need to show your work in detail. Is the 3.6 (meters) result supposed to be the height attained?

I said it's because even tho he/she ran for 30km/h achieved fairly low height (3.6m)

So, how might one clear a bar at 5 meters when one only has enough kinetic energy to raise one's center of mass to [an assumed] 3.6m?

 

[TomHart]

I think we agree that her height increased by 3.6 m, but you have to consider where the starting point is. Hint: 4.6 m is the right answer.

For part b, the problem is telling you that pole vaulters are able to clear a 5 m bar. Then they ask how that can be possible considering that she doesn't produce enough kinetic energy to be able to increase her center of mass to that height.

 

[Derek1997]

I really appreciate your helps guys, first off, I gone 1/2mv2=mgh cancell h and solved for h which I got 3.6m. But she has a starting height of 1.7m so 1.7+3.6=5.3m?

 

[Tom.G]

Have you ever seen a pole vaulting exihibition?
What is the body orientation of the vaulter when clearing the bar?
What sources of energy, other than legs, are available to the contestant?

 

[Derek1997]

Have you ever seen a pole vaulting exihibition?
What is the body orientation of the vaulter when clearing the bar?
What sources of energy, other than legs, are available to the contestant?

No, I haven't seen any pole vaulting or I did when i was really young. I guess hands?

 

[jbriggs444]

I really appreciate your helps guys, first off, I gone 1/2mv2=mgh cancell h and solved for h which I got 3.6m. But she has a starting height of 1.7m so 1.7+3.6=5.3m?

If she has a height of 1.7 m and jumps up by 3.6 meters, that gets the top of her head over a 5.3 m bar. Would that be enough?

 

[TomHart]

Derek, here's a YouTube clip of a pole vaulter in slow motion.

 

[Derek1997]

If she has a height of 1.7 m and jumps up by 3.6 meters, that gets the top of her head over a 5.3 m bar. Would that be enough?

Well since the record is over 5m, I guess it makes sense? so yes

 

[Derek1997]

Derek, here's a YouTube clip of a pole vaulter in slow motion.

Thank you Tom, but what confuses me most is the 4.6m part, I don't get it.

 

[BvU]

Make a sketchy drawing, showing clearly where the 3.6 m you calculated (correctly), is located ...

 

[Derek1997]

O

Make a sketchy drawing, showing clearly where the 3.6 m you calculated (correctly), is located ...

Okay then?

 

[BvU]

I expected a drawing, not a question. Okay what ?

 

[Derek1997]

I expected a drawing, not a question. Okay what ?

I can't upload it here man, But I am pretty sure I got it right(thats what I sketched) so assuming the bar is 5m he pushes himself 3.6m using spear since he is 1.7m tall he passes the 5m bar with 0.3m difference. right?

 

[BvU]

No. Passing isn't the word. The bar will hit her throat (it was her pole). if she stays upright.

 

[TomHart]

Hi Derek. Here is a YouTube video that describes the "Fosbury flop" high-jumping method. It's the method currently used by . . . virtually all high jumpers. It is a good visual description of the physics involved in high-jumping. Also, contrast the pole vaulter and the high jumper. Once the high jumper's feet leave the ground, there's nothing he can do to apply more energy to increase his maximum height - well, except for maybe trying to flap his arms like a bird. The pole vaulter still has his hands on the pole. Can he use that to any advantage?

 

[Tom.G]

I guess hands?

Yes!
Now, since you've seen the videos, when a body freely rotates, around what point in the body does it rotate?

edit: strike-out

 

[haruspex]

in the body

Did you mean to specify that?

 

[Derek1997]

What I did was 0.55x1.7+3.6= 4.6m So I got a
for B i said some energy concerted into heat also Air friction impacts as well.

 

[TomHart]

Part a looks right. But for b, the factors you mentioned would REDUCE the height she could jump. And actually, she is able to jump HIGHER than the calculated height of 4.6 m.

 

[Derek1997]

Part a looks right. But for b, the factors you mentioned would REDUCE the height she could jump. And actually, she is able to jump HIGHER than the calculated height of 4.6 m.

Wait so, for part B we have to say why she has to jump higher than 4.6m? if that's a case i guess techniques would help? eg hand postures and etc? am I right

 

[jbriggs444]

Wait so, for part B we have to say why she has to jump higher than 4.6m? if that's a case i guess techniques would help? eg hand postures and etc? am I right

What techniques, specifically?

 

[CWatters]

Hint: If her running/KE gets her to 4.6m she needs another source of energy to get to >5m.

 

[haruspex]

Wait so, for part B we have to say why she has to jump higher than 4.6m? if that's a case i guess techniques would help? eg hand postures and etc? am I right

Put yourself in her place. Your mass centre is at a height of 4.6m, but you have to get it up another 0.4m (well, maybe not quite, but we can discuss that later). You are still holding onto the pole. The pole is straight and vertical. The bottom of the pole is on the ground. What are you going to do?

 

[Derek1997]

Ohh, I think I get it now, it's easy you just stretch up your body and move ur legs first then and swing ur arm to pack it up and move from cross bar.

 

[haruspex]

Ohh, I think I get it now, it's easy you just stretch up your body and move ur legs first then and swing ur arm to pack it up and move from cross bar.

That might be right, just not quite clear what you mean. To clarify, where is the extra energy coming from in that?

 

[Derek1997]

That might be right, just not quite clear what you mean. To clarify, where is the extra energy coming from in that?

Extra energy technically isn't coming from somewhere, It's just saving of energy to use it in a good cause that is stretching more.

 

[haruspex]

Extra energy technically isn't coming from somewhere, It's just saving of energy to use it in a good cause that is stretching more.

I don't understand. Rising the extra 0.4m requires energy. It must come from somewhere.
What is being stretched, exactly?

 

[Derek1997]

It's because of COM, no COM more energy to raise ur body.

 

[haruspex]

It's because of COM, no COM more energy to raise ur body.

I have no idea what you mean.

 

[Derek1997]

Sorry for inconvenience, I meant since the center of mass wouldn't be within the athlete's body during the jump (he is in the air) hence, It's easier for him to cross the bar. Easier to move his legs and etc.

 

[jbriggs444]

Sorry for inconvenience, I meant since the center of mass wouldn't be within the athlete's body during the jump (he is in the air) hence, It's easier for him to cross the bar. Easier to move his legs and etc.

Can you explain why you think that any of that is true or how you think any of that works?

 

[haruspex]

center of mass

Are you considering the pole as part of that mass? If so, don't. We are assuming the pole's mass is negligible, and if we were to allow for its mass that will make it harder since some of the pole's mechanical energy will have gone into raising the pole to the vertical.

You are right that the athlete's mass centre may be external, but can you explain how, exactly?

 

[Derek1997]

Are you considering the pole as part of that mass? If so, don't. We are assuming the pole's mass is negligible, and if we were to allow for its mass that will make it harder since some of the pole's mechanical energy will have gone into raising the pole to the vertical.

You are right that the athlete's mass centre may be external, but can you explain how, exactly?

To maximize vault height, vaulters bend their body around the bar (as shown in the figure below). In doing so, their center of mass (the red dot) can actually pass underneath the bar, while enabling their body to pass over the bar (the black dot). This means that the bar can actually be placed higher than the maximum height reached by the center of mass of the vaulter.pole vaulters do not use their strength to lift themselves over the bar. Instead, they primarily use the pole as an intermediate tool to help them convert their kinetic energy into gravitational potential energy (height). Good sprint speed combined with good gymnastic ability are what is needed to effectively utilize the pole.Air resistance also plays a role in how high a vaulter can vault. In areas of higher altitude, the air is less dense which reduces air resistance when running. This in turn means that the vaulter can reach a higher speed before the vault, which results in a higher vault. To give you an idea, if a vaulter running at 10 m/s at sea level can run 2% faster at high altitude, then he can vault about 21 cm higher at high altitude. enough?

 

[Derek1997]

I hope that can explain part B?

 

[haruspex]

I hope that can explain part B?

That (passing the mass centre below the bar) is certainly part of it, but I doubt it would get another 0.4m. You are still missing an important component hinted at in several posts.
Look at the position of the vaulter's body in relation to the part of the pole the vaulter is holding. How does this change in going from ground level to going over the bar?

 

[Derek1997]

That (passing the mass centre below the bar) is certainly part of it, but I doubt it would get another 0.4m. You are still missing an important component hinted at in several posts.
Look at the position of the vaulter's body in relation to the part of the pole the vaulter is holding. How does this change in going from ground level to going over the bar?

Horizontal velocity to vertical velocity change?

 

[haruspex]

Horizontal velocity to vertical velocity change?

No, not velocity; position.