Applied Maths (Statics)

Mutant_Fruit

This is an old mock question.... its driving me insane.

Two rough rods OA and OB are fixed at right angles, OA is vertical. Two small rings of weights 3W and 4W can slide on these rods. The 3W ring is on OA, the other on OB. They are connected by a light string. The coffecient of friction is 0.5 (1/2).

Prove that in limiting friction the angle of inclination (theta), of the strings to the vertical is tan(inverse) 1.75. Find the tension also.

I marked in the info on this picture, fill in the forces etc on your own pictures.

Sev

Ok, well examine the forces on the 4W weight, at the point of slipping..

You have the weight, 4W, directed down, The tension from the string, and you have the friction.

The friction is equal to the normal reaction of the ring on the rod times the coefficient of friction, and we know the normal reaction of the ring on the rod is equal to the vertical component of the tension in the string (Tcosq) plus the weight of the ring.

So f1 = (1/2)[Tcosq + 4W]

And we know that at the point of slipping, the friction is equal to the horizontal component of the tension in the string

so f1 = (1/2)[Tcosq + 4W] = Tsinq

so 2W = Tsinq - (1/2)Tcosq

=> W = (1/2)Tsinq - (1/4)Tcosq

Now examine the forces on the 3W ring.

Theres the weight of 3W down, theres the Tension from the string, and then theres the normal reaction of the ring on the rod counteracting the horizontal component of the tension from the string. But then theres the friction on this ring too.. Theres a vertical frictional force up the rod. This frictional force is equal to the normal reaction of the ring on the rod times the coefficient of friction. And we know the normal reaction on the rod is equal to the horizontal component of the tension in the string (Tsinq).. so

f2 = (1/2)Tsinq

And since the system is in equilibrium but on the point of slipping we know that the vertical component of the tension in the string and the upward frictional force is equal to the downard weight of the ring.


f2 + Tcosq = 3W
(1/2)Tsinq + Tcosq = 3W

=> (1/6)Tsinq + (1/3)Tcosq = W


Now combine this with our previous result that..

W = (1/2)Tsinq - (1/4)Tcosq

and we have

W = (1/2)Tsinq - (1/4)Tcosq = (1/6)Tsinq + (1/3)Tcosq

=> (1/2)TSinq - (1/6)Tsinq = (1/3)Tcosq + (1/4)Tcosq
=> (4/12)Tsinq = (7/12)Tcosq

=> Tsinq / Tcosq = 7/4
=> Tanq = 7/4

I hope that helps.. good luck with your mocks and in the LC.

jackwalli

MutantFruit - Statics is the most evil question on the paper. Closely followed by Q8. At least that normally has a proof which you can learn off beforehand. Have you picked your 6 most likely questions yet?

PrecariousNuts

1 definitely
2 should be ok aswell
3 you bet
4 hopefully it will be a nice one
5 same
10 usually alright.

I'll try 6 and maybe 8 just incase

Is it just my papers or have yours got the answers in the back? It drives me crazy when they are not there

Sev

Dont get too over confident with Question 1. I know it can be very easy, and it looks easy, but make sure youre familiar with answering it, dont take it for granted. Last year's Question 1 part (a) was quite tricky indeed, it took me the entire exam before I copped it.

jackwalli

Sevs right about question 1 - sometimes they take me an hour or more to do, and even then they're usually not right.
Question 2 is usually the same kind of thing every year, I've just got to revise it more.
Question 3 is soooo sweet. I dont think I've ever seen a hard question 3, or any major variations on the standards. The only dodgy part is if theres one or more bounces.
Question 4, gorgeous, the worst they can do is give a set of weights on a pulley on a wedge which is on a surface where there's friction, and even then its doable.
Question 5, usually pretty good, apart from the "Prove that..." which i find really hard sometimes.
Question 6 I havent revised yet but I think I'll be doing it since i don't have many other options.
Question 7,8 and 9 i hate and will try to avoid if at all possible.
Question 10 is usually ok, but i keep forgetting the differentiation/integration techniques, needs a lot of revision, but again, questions are all very predictable.

I've got Educational Company Papers, no solutions in the back, but they do go from 2003 to 1989, which is way better than most subjects. I've got marking schemes for most questions (1,2,3,4,5,10) back to 1984 if youre ever stuck.

Mutant_Fruit

Yeah. I was doing the question earlier, and when i compared it to your workings, i realised that i forgot one thing

I forgot to set mew (coefficient of friction) = Friction/(Normal reaction). Once i did that for the two particles i solved the thing in about 5 minutes. I feel like an idiot.

As for the questions i chose, here's it so far.

Q. 1) (Linear Motion) Probably, but you can;t rely on it. There is so much variety that sometimes its extremely hard, others it's easy.


Q. 2) (Relative Velocity) Easy, easy, easy. Anyone who doesn't do this needs a head check. It rarely changes.

Q. 3) (Projectiles) Easy aswell. Its all method. You always call the angles alpha, or alpha and beta. Everything is predictable. If you can do the last few years, you can do them all.

Q. 5) (Impacts and collisions) Generally this is easy. If you can do one, you can do them all. The tricky part is interpreting the question correctly. Once again, this is all method, you do the same things every time.

Q. 6) (Statics) I fail to see why people hate this so much. Statics is easy when you get the hang of it. All you ever do in it is draw a diagram, insert forces (they are only Normal Reactions, Frictions, Tensions and Weights). Once thats done, all you do is balance the Ups with the Downs, and the lefts with the rights and then take moments about any point.
Assuming that you can decide what an Up force is, and what a Down force is, theres no way you can go wrong with this. The only (moderately) hard thing is taking moments.

Q. 8) (Moments of Inertia). At first i thought this was extremely difficult, but after doing 5 years worth of questions, everyone in my class is now agreeing that this is a definate question. 20 marks of every question is given for proving the formulae in the maths tables. You can do this very easily. The remaining parts of the question generally are related to the part A (the proving the formulae bit) and aren;t too difficult once you've seen a few.

correct me if i got the wrong question numbers beside each topic title, but i think i got em right.

jackwalli

Mutant_Fruit:
Becareful with question 8 - you're not always asked to prove the formula from the logbook, and sometime they even ask you to prove formulas for things like triangles (you'll see that on in Fundamentl Applied Maths, by Oliver Murphy). Just dont rely on being asked a proof in that question.
What books do people use for the course? Right now Ive got Fundamental Applied Maths and another newer one Applied Mathematics for Leaving Certificate / Foundation Mechanics for Third Level by Kevin Conliffe - the second was only published in 2002, has some great formulas and unique methods in it, well worth a look. The older one is a lot more comprehensive in its examples though. For some reason im feeling pretty screwed for this in the leaving though, dunno why.

I fail to see why people hate this so much. Statics is easy when you get the hang of it.

- Thats the problem - I found it really hard to get a hang of - in 4th Year and this year too. The problem im having now is that i relaxed through leaving cert so far since i finished the course around easter last year. Im ruling out every 2nd question, so now Ive only got a bare 6 that im "good" at. And i use the term "good" very loosely.

If you like question 8, you should love question 4 - all just forces and tensions - should be a nice one. Question 8 ive always hated because of this bollocks of a question in our book about rings on wires, that i never got and now i cant even bare looking at it.

Sev

Well, just saying sometimes what are usually easy questions can sometimes be quite tricky. For example in question 1, like in last year, you may have to cop something not expressly stated in the question for the question to work.

Question 2 can be ugly if it involves men swimming across rivers that move faster than them, make sure you can do those questions.. how to find the optimal angle to cross the river fastest (easy) and the optimum angle to cross the river without going too far down stream.

Question 3, projectiles are trickiest when you are required to prove some really ugly looking identity with tans cosines and stuff, sometimes it can involve the use of obscure trigonometric identities, little tricks like that and flexibility with manipulating trigonometry to get it out right. They can also be tricky if they ask, like, what direction must the particle be fired such that it just clears the wall on the way up? or how far up the ramp does it go such that it lands perpendicular.. etc..

Question 5: Can be awkward if its like last year's, twice I had thought I had finished the question, then only realised I had forgotten one factor that made it a hell of a lot more complicated, it was something about one ball.. hitting another ball.. hitting a wall.. coming back and hitting another ball again... so you can see how that can get very long, tedious and involve lots of constants of restitution getting bounced around as well as some ability to manipulate the equations such as to reduce the ugly mess to make it look like the answer youre supposed to get.

Question 6 (Circular motion + SHM) : I liked this question if its just SHM, and was usually manageable, usually just involves plugging values into the Acos(wt) function, knowing how to differentiate it to work out the velocity, and knowing that wA is the max velocity and knowing max stored energy (max kinetic energy) etc.
But.. I stayed well away from this if it was circular motion, the regular plane circles are nice, but Id advise making sure you know how to work with motion in a vertical circle.. its just plain nasty, and know how to do that god awful question with the bead rolling off the sphere, and having to work out at what point it leaves the surface. Also take a look at that question with the rings on the hoop like in 2002.

Question 7 (Statics): I ****ing hated this one. The reason being, that although most of them are manageable in time, and I'll work them out eventually, I just never had the familiarity and technique to solve these kind of things quickly and without forgetting things like vertical friction. It can be a headwrecker of a question if youre leaving something out. If youre planning on doing the statics question.. get very familar with it.

Question 9 (Hydrostatics): Similar sentiments, if it involves statics and stuff, but sometimes it can be easy if it just involves pressure and density and stuff and archimedes laws. Last year's one was a bit off the wall, I stayed well away, Id advise trying that one if youre planning on doing Q7. But I never liked that rod resting on the edge and floating in the water at an angle, with the question.. how much of the rod is submerged?.. but make sure you know how to answer that, cos it comes up alot.

Question 10 : My favourite question ever... that said I thought every one of these questions was perfectly predictable coming up to my leaving cert last year.. but last years 10 was new to me. So make sure that not only can you do these questions if it just involves forces and acceleration etc. but know how to do the questions that involve understanding Power, Work/Energy, and friction etc, like that one last year. In fact they can throw in all sorts of different types of quantities into those questions, as long as theyre quantities that can are expressed as the rate of change of another, but I wonder what is technically on the syllabus, cos there are ways of making that question very complicated. But dont let that worry you, just know how to do that question whatever the hell is involved.

For my leaving cert I never studied Question 8 (Moments of inertia), I went into my exam with my 6 strongest questions being 1,2,3,4,5 and 10. And In the exam, I did 1,2,3,4,5 and 10

Nike_Dude

I only went for questions 1, 2, 3, 4, 5 and 10 last year I didnt really have much choice since I was trying to do the course in one year.
As Sev said all the questions can turn nasty, especially Q.1 and 2. Just make sure you can at least make a decent effort at any variation of the questions that might come up

GooglyEyes

Gonna be picking my subjects for my L.C. soon, but I dunno wat i wanna pick..

I got an A in honours maths for my junior cert so I'm thinking of picking applied maths. Would anybody advise against this?

Is there a lot to cover in the course? Would I be crazy to pick it as an extra subject?

Making It Bad

GooglyEyes wrote: »

Gonna be picking my subjects for my L.C. soon, but I dunno wat i wanna pick..

I got an A in honours maths for my junior cert so I'm thinking of picking applied maths. Would anybody advise against this?

Is there a lot to cover in the course? Would I be crazy to pick it as an extra subject?

This thread is from 2004, you'd be better making a new thread.

Geog ariphic

Please can someone give me a link to applied maths proofs, or just the ope for prooving the centre of gravity of a triangular lamina is the centroid?? Im desperate!