wedge/ connected particle Q.

sd123

can anyone help with the 1993 applied maths Q4. I cant do it and ive been told that it was a real stinker. is there a reaction at the right hand side of the wedge? anyway if someone could post the answer it would be great

enda1

Why not post a link to the question or the question itself and someone may be able help you.

JC 2K3

It's the hardest relative accelleration question they've asked in the last 20 years or so.

I tryed it and couldn't get it, however, on reviewing my answer I realised I'd forgotten that the strings pull on the wedge(I guess you resolve the tension in that direction).

I wouldn't worry too much if you don't get it, there won't be a question as hard on the actual paper. Wedges are a weak point for me, but any wedge Q asked in recent times(last 5/6 years) has been písstakingly easy.

ZorbaTehZ

Hello SD123, and welcome to Boards.ie and the Leaving Cert Forum.

SOLUTION:

F=ma Equations of the Particles/Wedge:

1. 12g/5 - T = 4(f - 4g/5)
2. 16g/5 - R = 4(3a/5)
3. T - 2g = 2f
4. F = 2a
5. 3R/5 - 4T/5 - F = 10a

Where:

T is the tension in the string.
R is the perpendicular reaction on the particle on the inclined side of the wedge.
f is the acceleration of particles connected by the string.
a is the acceleration of the wedge.
F is the reaction on the right side of the wedge.

Manipulate Equations 5, 3 and 2 for an equation in f and a only.
Which is:
8g = 336a + 40f

Manipulate Equations 1 and 3 for an equation in f and a only.
Which is:
2g = 30f - 16a

Simultaneous equations:

336a + 40f = 8g
-16a + 30f = 2g . . . . (-4/3)

336a + 40f = 8g
64a/3 -40f = -8g/3

1072a/3 = 16g/3
1072a = 16g
a = 16g/1072 = g/67. . . QED

ZorbaTehZ

POINTERS:

sd123 wrote:

. . .is there a reaction at the right hand side of the wedge?

Read the question again:

. . .which hangs vertically and touches the side of the wedge.

Would it say that if you didn't need to consider a reaction on the right side?;)

As a wise man once told me, you can consider reactions everywhere on all the particles, if they're not in the system then they will come out as zero in the end - but it's when you don't consider a particular force/reaction that you'll end up making a mess of the question.

JC 2K3 wrote:

. . .on reviewing my answer I realised I'd forgotten that the strings pull on the wedge(I guess you resolve the tension in that direction).

The two things that you need to 'get' before you can do the question is, like you said, the tension in the strings reacting on the wedge and the reaction at the right side of the wedge.

SD123 anymore questions you can reply here or you can use the pm system.

JC 2K3

Cheers for the solution Zorba. I attempted that Q without having practiced easy wedge questions first. I must go back and try it again, but your answer will no doubt help.

cocoa

aha, but my solution has pictures!!! SOLUTION <--clicky clicky

edit, ah yes, hotlinking... gimme a sec... >_> there fixed....

ZorbaTehZ

Aye, 'twould be nice if the link worked too mate.;)

sd123

Thanks a mill with the answer. I'm sure it will come in handy! here just as a matter of interest can i just throw out a question. Have most of ye done applied maths for two years. I only started in Nov this year and its coming on ok (i hope). its just that my school only offers it evry 2nd year. What's the chance of me doing anyway well. (only 6.5 - 7 Q's done)

JC 2K3

You'll be fine if you work at it.

I had a class last year(with cocoa), didn't really work that hard but picked up the basics. This year the class has disbanded because too many people dropped out so I'm doing it on my own now.

I only know 6 Qs well - 1-5(Linear Accelleration, Rel Vel, Projectiles, Connected Particles/Wedges, Collisions) and 10(Differential Equations). I also know the basics of Q7(Statics) and hope to cover Q9(Hydrostatics) before the exam.

If you know 7 Qs well you'll be fine.

ZorbaTehZ

Make sure you're atleast familiar with all topics if you're aiming for an A1. It has happened before, as you can see from past papers, that things like SHM have come up in Statics questions and even in Connected Particles questions.

JC 2K3

^All? Nah, 7 is grand, I'll probably know 8. Yes they do sometime mix questions, but since SEC took over that seems unlikely, and they definately won't mix topics on more than one question.

Although if by "familiar" you simply mean have a fundamental knowledge of what they involve, then I agree.

sd123

thats grand. yea i have 1/3-6 10 and half of 2. if i was to try to get another done before the exams, any recommendations on quick questions working only out of the book. thanks again

ZorbaTehZ

You could try make a start on question 7 which is Statics. Much of it is based on the reactions involved in question 4 and also on moments, however it is a question that takes some getting used to.

JC 2K3

To quote cocoa, "I've said it before and I'll say it again, do hydrostatics(Q9), it can be a very easy question".

Hence me intending to learn hydrostatics.

I'm not a fan of Statics.

cocoa

sd123 wrote:

thats grand. yea i have 1/3-6 10 and half of 2. if i was to try to get another done before the exams, any recommendations on quick questions working only out of the book. thanks again

I'd recomend 7 and/or 9 (statics and hydrostatics). To be honest I'm a little surprised you went for question 6, considering it involves both circular motion and simple harmonic motion which means more learning but anyway...

Once you get used to them, both statics and hydrostatics can be very straightforward. Statics changes very little but can sometimes be difficult due to some slight spin on an old scenario or the equations being a bit messy.
Hydrostatics, on the other hand, involves learning more formulae but can sometimes be an absurdly easy question. Definitely worth looking over but if you were going to count it as a definite question you'd need a little bit of practice with partially immerse rods/laminas and harder questions like that.

Have you looked at question 2 (relative velocity) much? I know come people have big problems with it but for me it tends to work out nicely for me without too much work.

Finally, if you want a question which involves a certain amount of rote learning, but as a consequence means some relatively certain marks in the exam (and therefore a little confidence boost) then you might like question 8 (rigid body rotation) which has a number of proofs and plenty formulae, but tends not to be too complicated.

Personally, I've had a good look at all questions but on the day I will probably do one of 1-5, 7, 9 or 10.

fuinneamh

out of curiosity which book do you use? kevin conliffes, "Applied Mathemathics or oliver murphy's "fundamental applied mathemathics" ?

cocoa

oliver murphy's "fundamental applied mathematics". It's alright to give you the basics, but it doesn't IMO give enough examples and there's a few questions in the exam papers which are very tricky if that's all you've got to work off of...

ZorbaTehZ

Ollie's book ofc. I've heard the other one is a bit sucky though tbh.

sd123

I use fundamental applied maths. I heard the other one isn't great. ANy way thanks for the suggestions. I think i'll go for hydrostatics cos least amount of people do it and therefore might be a bit easier. The only reason i went for the q6 shm and circular was because i have alot of the basics done in physics but the SHM questions can be very difficult with two elastic bands and stuff. The one thing that i have difficulty with in q2 is when sometimes they ask to get the relative velocity. when i get that it might ask for the shortest distance in subsequent motion. so you let one stay at the origin but only get one point for relative velocity. does this mean the ship/ car etc moves in a straiht line connecting the origin to the point?

cocoa

sd123 wrote:

The one thing that i have difficulty with in q2 is when sometimes they ask to get the relative velocity. when i get that it might ask for the shortest distance in subsequent motion. so you let one stay at the origin but only get one point for relative velocity. does this mean the ship/ car etc moves in a straiht line connecting the origin to the point?

yes, unless you have relative acceleration, which you really shouldn't considering it's relative velocity.

oftentimes it's handy to remember that if you want an interception, the j velocities of the two particles must be the same.

Gangsta

isn't applied maths the best subject in the world:)?