Harshini's post has brought back a few things from when I was a kid. One of the first things that brought to my mind the thought of becoming a scientist was the cartoon Dexter's laboratory. My interests did change but it did invariably come back to physics. I actually even wanted to be a wildlife photographer in 9th standard, but then I realized photography(and for that matter anything else) wasn't really my cup of coffee.
You find dexter( and some times tom and jerry) mixing up these random chemicals and colourful liquids and surely enough there would eventually be a big bang.I told my mom to get me one of those and she told that they are just cartoons. And then at school in 8th std. , I first heard of an actual explosive chemical reaction. When you put sodium in water it is supposed to react violently and can also be explosive, and our chem teacher said she is going to show it to us in lab. She ended up putting a tiny bit of sodium in water and all you could see was a tiny bubble of fire. And then I thought may be this was as 'explosive' as it gets in real life. I was a bit disappointed.
A few years later I was helping these people build up a lab( for school kids ) and I told them to buy a few things including sodium. I used to get a lot of time alone there to come up with experiments that would excite kids and once my school mate Sneha was around to help and everyone else had gone to have lunch. I slowly slipped in the idea of trying out the experiment with sodium. I was actually scared of doing it alone and also I wanted a partner in crime if something went wrong.
We filled a small glass beaker with water and I just took up a chunk (as big as a match box!) of sodium and put it in the beaker. Before we could see what was happening , small glass pieces were flying everywhere and the water just vaporized with a huge bang. This is a very memorable event, because a) this was the first time I saw an explosive reaction I had read so much about all through my chemistry classes and b) Not a single glass piece touched us. That actually left us shocked for quite a while. There was not a single place in the room where the glass pieces didn't go, and I had almost no time to move away after putting the sodium. It was pretty unbelievable. For once I wished my lab teacher was around shouting at me as usual to put on the safety glasses which I conveniently forget to carry to college. But I guess we just got lucky and lord murphy was on a holiday I suppose.
After that we used plastic buckets filled with water and put larger chunks of sodium and we showed every kid who walked through the door what " Smoke on the water and fire in the sky" actually looked like.
After experiencing a completely institutionalized learning at college and school, it is really refreshing and revitalizing when things are experienced and learnt in any unconventional ways.
All through school and college we are made to solve problems so that we can get more marks, or get through an entrance exam and have an amazing life ahead. But that's not why take up problems to solve, now is it? So lets try to solve some nice problems just to have fun. I will be posting up a problem as regularly as I can, and Harshini said she will be too. Please do try to spend a few minutes thinking about them, I'm sure it will be worth it. Solutions will be put up eventually. Here is the first one, enjoy :-)
When told that the world record for the pole vault was about 18 feet, the fast-rising athlete Rod told the press, 'Give me a pole long enough, and I will raise the record to 30 feet'. Could he manage it? How high might he get if tried hard?
Interestingly I have been doing bit of pole vault
ReplyDelete(not on the play ground but around the terrain near my house).
What I figured out is the height to which I go depends on how fast I run, I also figured out that I need to have a long stick. And I need to grab it at the tip as high as possible, I would wish I could be a little taller.
So basically I feel how high I would get depends on how tall I am and how fast I run. May be even a longer stick would help , but the issue is it cannot be indefinitely longer.
Let us look at it this way, all what you are doing is converting K.E into P.E.
So the point is there is a limit to which you can pump K.E, which is basically the speed at which you run. which has a limit. So there is a limit on the P.E.
Which means there is limitation to the maximum height that can be attained.
However if you take a longer pole there is some issue with the angle of take off, right now cannot figure out what exactly would be the problem, if I do i will get back :)
Looks likes I have some idea. The point is when you have a reasonably long stick you basically keep it at a point which is optimum ( not very far from you not very close to you) so that you can bend it to the maximum.
ReplyDeleteBut if you have a stick which is too long, then you will have to keep it very far away from you if you want to bend it any more ! For that you need to be much taller !
So the height of the stick has some correlation to your own height I feel.
So Mr.Rod may not be able to do this with his height and speed of running I think, I have not done the calculations yet, I generally work with intuitions better, so shall I leave the calculations to the theoreticians or enthusiastic youngsters ? :)
( I am lazy with equations I guess)
as we all know, to leap over the pot holes in the roads of bangalore during rainy season, we need to "gear up" before we take the leap. something similar happens in pole vaulting{only that there is a pole for aid---also in this, height matters over the covered distance}.
ReplyDeleteNow the kinetic energy of the vaulter is transferred to the "spring energy" of the pole {i.e, assume ideal conditions that he's the best runner, pole only transfers energy and no energy goes WASTE}. the spring energy is again transferred as the PE of the vaulter. Now it's simple!
(1/2)mv^2=mgh. now since we know the total height (30 ft--approx 9m), subtract from this his center of mass ht (approx 0.8m--half of avg ht 1.6m) , we get h=8.2m. now apply the formula and get v. we will be surprised that the value of v which we get is above than that of the fastest sprinter's record(~10m/s--looked up in the net!!). Now, for the vaulter, he has to carry the vault also. so, his v is much less than that of the "free" sprinter. so, i think he can't.
oh!! I had not read satyajith's analysis. just typed in my "calculations".
ReplyDeleteWhile the phyics of pole-vaulting essentialy rests on the conversion of kinetic energy into potential energy, I am left to wonder about Mr. Rod's statement on breaking the existing record to 30 feet -- is this proposed new record 30 ft some "limiting height" that could ever be reached? Physics of pole-vaulting doesn't indicate any PRECISE limiting values as such!
ReplyDeleteOh I think it is just a randomly picked high value which corresponds to the speed of fastest runner in the world( as karthik's calculations point out), hypothetically there may not be a limit, but practically it does exist, does it not madam ?
ReplyDeletewhat I mean is: corresponds to a value just above the speed of the fastest runner on record.
ReplyDeleteYes -- I agree with you Satyajit. (One should remember that it is an athlete who made this statement -- not a scientist!!)
ReplyDeleteHere I post a American Institute of Physics link on the physics of pole vaulting: http://www.aip.org/png/html/polevault.html
30 ft vault height is acheived by entering a sprint speed of 28 m/s and height of the Vaulter as 6.5ft! I should say Mr. Rod is highly unrealistic (I didn't say unscientific -- because physics allows this limit)!
Hi Guys,
ReplyDeleteI went over the responses & i found my explanation very similar to Karthik's. But wanna
point out a few extra things to it...
First of all lets go over the principle, A pole vaulter runs building his K.E., he transfers it to the pole immediately when he points the pole on the ground hence transferring all his K.E. to P.E. in bending the pole & the pole again transfers the P.E. to the person raising him to a height.
Considering the pole is perfectly elastic & no energy is lost in the process, we have
1/2(mv^2)= mgh
i.e. 1/2(v^2)=gh
h=1/2g(v^2)
lets consider a case where a pole vaulter runs at 10m/s & g=10m/s^2
we get h=5m
also we need to consider the height of the person...lets say for simplicity of calculation his height is 2m, so his centre of mass would be 1m approx.
Taking this into consideration the person can jump to approx. 6m which is about 19.6ft, whereas the current world record is 6.15m =20.2ft.
Also if u notice in the above formula, there is no relation b/w height of the pole & height acheived by the pole vaulter, whereas the mass of the person also deosn't matter. In the olympics generally a pole of 10 to 15ft is used & also the athelete holds the end of the pole the raise up as high as possible & to have a balance. But if we go over the equation, the person will be raised to only how much work he does on the pole, so it does not matter how long the pole is. Suppose a person wants to make a 30ft jump(9.14m), subtracting his height we get that he must achieve a height of 8.14m. Substituting this in the equation we get that he must run with a velocity of 12.75m/s which is not possible be humans as of today:)
ReplyDeleteThese equations are only simplifications. Obiviously it is missing something. You cannnot have a two feet pole and jump that height neither can you jump it with a fifty feet pole !
ReplyDeleteThere has to be a definte relationship between the person's height and the pole's length.
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ReplyDeleteYou're right in a sense that u cant jump with a 2ft pole, but the pole of height 15ft is chosen to jump a height of about 20ft. If u've seen the sport u would have noticed that at the end of the jump the PV propels his body upwards, taking the support of the pole, thats it. In case(which is not possible) the PV were to jump a 30ft crossbar, he would use a 25ft pole, but would have to run with speed of 12.75m/s which is not possible.
ReplyDeleteHowever, there is a relation b/w the person's weight & the stiffness of the pole. Lets consider 2 ppl 1st weighing twice the 2nd & if they wanna produce the same amt. of bend in the pole. The pole used by the 1st person must be twice as stiff as the pole used by the 2nd.
you have written "but the pole of height 15ft is chosen to jump a height of about 20ft"
ReplyDeleteThis choice is made keeping in mind the height of the person. Hypothetically if there was a person one foot tall, he would not be able to handle a long stick because where he grabs it gives him the take off. Which means there is a correlation between the person's height and the pole height.A tall sprinter can hold the pole higher to achieve a greater gravitational potential energy than a shorter sprinter, which basically means the pole has to be that much longer if he has to do it. But generally people's height do not differ so much so, more or less the same pole can be used, but in principle there would be a difference.
I did mention in my one of my 1st posts that "In the olympics generally a pole of 10 to 15ft is used" :P
ReplyDeleteIf we also consider the mass of the pole, and apply conservation of energy at instant 1 (just before take-off) and instant 2(when the athlete achieves maximum height), we'd get something like
ReplyDelete1/2(m1v1^2) = m1g(h - L1/2) + m2g(L2/2 - d)
where m1 : mass of the athlete
v1 : maximum speed attained by the athlete
L1 : height of the athlete
m2 : mass of the pole
L2 : length of the pole
d : height of centre of mass of the pole from the ground just before take-off.
h : maximum height attained by the athlete.
assuming that the centre of mass of the athlete lies at half his height.
Assuming a uniform mass distribution for the pole, we can substitute m2 = k(L2)
where k is the mass per unit length for the pole.
If we now solve for h, we get something like
h = c1 + c2(L2) - c3(L2)^2
where the parameters m1, v1, L1, d and k have been absorbed in c1, c2 and c3.
This parabolic relationship between h and L2 suggests that as length of the pole is increased, the maximum height attained first increases, then reaches a maximum value at a certain optimal pole length. Beyond this optimum pole length, the height attained would decrease again (provided all the other parameters remain unchanged).
This seems to make sense, because as pole length increases, so does the mass of the pole. And therefore, the athlete has to invest more and more energy in raising the pole.
But as there is an upper limit on the physical ability of the athlete, there must be a corresponding upper limit on the viable pole length, beyond which it becomes a liability.
So an arbitrarily long pole is not going to help Rod the athlete.
Interesting..thanks :)
ReplyDelete