Applied Maths, a question for the smart people

penguincakes

1997, 5 (a) A smooth sphere P, of mass m, moving with speed ku collides directly with a smooth sphere Q, of mass km, moving in the same direction with speed u. P is brought to rest by the impact.

i Find the velocity of Q after the collision in terms of u.
ii Prove that K >= 3

Ok now part i is alright (v=2u) but I don't have a clue how to go about part ii. It's either something stupidly simple that I'm missing completely, or something pointless & annoying. Either way, can anyone shed any light on it?

Mutant_Fruit

wait til i grab my papers.... this'll be the first applied mahts i've done in about a month

EDIT: Double check your veolocities....

DS

Well you know you've got to use the e formula, because you didn't need it in part i. So your expression for e is:
e = -(-v)/(ku-u) = 2u/(ku-u) = 2/(k-1)

Obviously, e is always <= 1, or else the law of conservation of energy is a joke.

2/(k-1) <= 1
2 <= k-1
k >= 3

Mutant_Fruit

Got it. You end up getting

2u = e[ku - u]

Therefore in a perfectly elastic collision (when e=1), you end up getting k=3. But e<=1, therefore for this to remain true k>=3, because as e gets smaller, k has to get bigger to retain the equality
qed

EDIT: damnit, i was beaten to it.

penguincakes

Originally posted by Discharger Snake
Well you know you've got to use the e formula, because you didn't need it in part i. So your expression for e is:
e = -(-v)/(ku-u) = 2u/(ku-u) = 2/(k-1)

Obviously, e is always <= 1, or else the law of conservation of energy is a joke.

2/(k-1) <= 1
2 <= k-1
k >= 3

Ahhh clever. Or I stupid. Whichever Thank you!

subway_ie

Bah. I haven't done one of those in at least 6 weeks. So screwed.

article6

If in doubt on question 5, remember to use both of your collision formulas in whatever way you can. It worked for me last year.

Also, your log tables are your best friend.

Mutant_Fruit

AS was said above... ALWAYS USE ALL YOUR FORMULAE! you should do that for one reason, and that reason is that you are then guarenteed to have taken at least 1 step in the right direction, and will get some good attempt marks.

By following the usual method that you do for every question, and filling in to all your formulas you can guarentee yourself 30 out of every 50 marks (nearly). Thats not half bad at all now, is it?

subway_ie

If you're *really* desperate, then just write down all the formulae you can remember, eg. in question 1, write down all of Newtons equations of motion and any other methods you can remember. Even if you can't attempt the question, you could get 10-15 marks. Can be useful in a timing disaster, or if it's a realy bad paper (or both even :dunno: )

Mutant_Fruit

don';t talk like that! It'll be a nice paper. Nothing to tricky (hopefully).

subway_ie

Well, at least when you're anticipating the worst possible paper, then you can't possibly be unprepared on the day. Unless it's even worse than I imagined, then we're all well and truly fecked.

article6

Subway's right - writing down the relevant formulae in Applied Maths (and probably in other number subjects as well) earns you marks. It could be worth 10 points to you on results day...

penguincakes

Originally posted by article6
If in doubt on question 5, remember to use both of your collision formulas in whatever way you can. It worked for me last year.

Also, your log tables are your best friend.

Aye how right you are, I used to loooove q5, almost always got them all right, I think I just need to get back into the hang of it again. ...like everything else...

DS

Generally if they ask you something that seems very complicated, the only hard bit is figuring out the first step and the rest is a cakewalk, like in that Q. If they ask you an inequality in Q5, it'll either be e<=1 or if you're told the direction after the collision you just say v<0, that kind of thing. You need to be on your toes for this paper though. We're guaranteed one or two "leap of faith" type questions where you need a bit of intuition. With 6 questions though, of all the A1s people are gunning for it's got to be the easiest. Pity not every school does it, every hons maths student should do it. It's not going to take up much time, and it makes your maths skills so much stronger.

subway_ie

Originally posted by Discharger Snake
Pity not every school does it, every hons maths student should do it. It's not going to take up much time, and it makes your maths skills so much stronger.

Most honours maths students struggle with the work they have to do for honours maths, never mind adding on applied maths. It's a nice, short course where most people get over a C1. But the only reason why people are getting such good grades in applied is because people only do it if they have a talent for maths.

DS

Yeah fair point, it's not for everyone, but there's a lot of people in my maths class who really should be doing it, rather than something gayly big like history or biology.

subway_ie

Originally posted by Discharger Snake
Yeah fair point, it's not for everyone, but there's a lot of people in my maths class who really should be doing it, rather than something gayly big like history or biology.

Yeah, there are a few like that in my class. But, to be honest, I'd prefer if they stay where they are. The small classes (8-12 people) were really great and a big part of the reason why we got the course done and revised so fast. If we had been in a normal class of about 30 people then I don't think we would have done as well as we have,