Mechanics Issues (1 Viewer)

[Abtari]

hi all,

we have just been taught mechanics before the school holidays, well not really taught considering a wad of exercise sheets and questions were simply dumped in front of our faces without much theory at all. newayz, so i am having considerable difficulty dealing with what we are actually required to know from the mechanics module. (i am not talking about circular motion, conical pendulum, motion around a banked circular track - We have just been asked to do some sheets on resisted motion, and mathematical/physical representation of motion).

i don't know what we are supposed to know from these sections and to what extent we need to know the harder 3unit projectile motion and simple harmonic questions. any indications would be great help. thanx heaps.

 

[who_loves_maths]

^ perhaps if you could be more specific then we can be more helpful. eg. give us an example of the sort of question you have to do?

however, in general, it is certainly advisable that you know a bit of 3u mechanics before starting on 4u, since in 3u you are usually taught the basics such as dv/dt = d(0.5v^2)/dx , etc...

so knowing these basics would certainly help you in 4u mechanics i would think since more of the things in 4u mechanics are probably derivable and doable systematically if you know how to operate with differential equations and other transformations... these are the basics from which 4u mechanical theory is derived anyway.

however, i doubt you'd need specific theory such as projectile motion when doing 4u mechanics (i'm not sure because i haven't done any 4u mechanics yet at school, but i have seen some mechanics questions on this BOS forum already concerning resistance motion - they don't seem that hard if you know the 3u stuff).

but in short, the more you know about it (3u or 4u), the easier the answers to questions will come to you.

 

[Abtari]

i wasn't talking about whether we needed 3 unit to do 4 unit mechanics or not...

i was just wondering what key concepts had to be known by students at the end of the mechanics module since our teacher - like i mentioned previously - did not do a very good job of letting us know what we needed to know (if you know what i mean). i.e. at the completion of the mechanics topic what we should have learnt.

since you havent started the module, it would be difficult for you to answer this question. neway, i also wanted to know how much of harder 3 unit (projectile, simple harmonic motion) was necessary as part of the 4 unit mechanics course.

 

[who_loves_maths]

^ okay... i misunderstood. but, resistant motion is a 'separate' topic to the mechanics of 3u in the sense that the type of motion is differnt so methods concerning SHM or projectile motion will not necessarily be useful to know in 4u mechanics. hence, it's not necessary that you have mastered 3u mechanics in order to do 4u mechanics (ext. 2 is just an extension of 3u, it doesn't necessarily mean the topics are harder, etc...)

however, 4u does depend on the fundamentals of mechanical differential equations which are learnt at the 3u level...
eg. like what i said in my last post: things like dv/dt = d((1/2)v^2)/dx, and other things like integrating repeatedly to get to the expression x = f(t), etc...
these are the fundamental concepts that you need to know for a study of any mechanics topic whether it's in 3u or in 4unit.

 

[Abtari]

i fully understand what you mean when you say that one needs to know fundamental transformations and methods of integration and formulae that are in 3 unit to do problems in 4 unit. after all, it is an EXTENSION of three unit.

i also understand what u mean when u say resisted motion is a separate topic to the mechanics of 3u since we neglect resistance and so forth at 3 unit level. yes.

however i dont necessarily agree with the statement "it's not necessary that you have mastered 3u mechanics in order to do 4u mechanics (ext. 2 is just an extension of 3u, it doesn't necessarily mean the topics are harder, etc...)".

u see, the thing is that 4 unit students are SUPPOSED to know how to answer harder problems on projectiles and SHMs. that is why i was getting concerned. so ok, we have to know how to do harder 3 unit projectiles and shms at 4 unit level...but how much harder, i.e. as i said in the first post, to what extent.....

its just that the mechanics module is so frustratingly ambiguous and convoluted. why do i feel like im the only one that hates this topic. prolly the teaching factor i guess.

thanks.

 

[who_loves_maths]

Originally Posted by Abtari
however i dont necessarily agree with the statement "it's not necessary that you have mastered 3u mechanics in order to do 4u mechanics (ext. 2 is just an extension of 3u, it doesn't necessarily mean the topics are harder, etc...)".

u see, the thing is that 4 unit students are SUPPOSED to know how to answer harder problems on projectiles and SHMs. that is why i was getting concerned. so ok, we have to know how to do harder 3 unit projectiles and shms at 4 unit level...but how much harder, i.e. as i said in the first post, to what extent.....

your being very presumptuous (line in bold)... why do you say that in 4unit you are "SUPPOSED" to know how to answer problems on projectiles and SHMs??? SHM and Projectile Motion are strictly 3 Unit topics, there are no "harder" SHM or Projectile Motion questions in 4u because 1) those two topics are not part of the 4u course, and 2) the question are not harder since they involve the SAME amount and quality of theory on the two topics as is taught at the 3u level... there are NO additional theory components on SHM and Projectile Motion at the 4 unit level.

so you don't make sense when you say "so ok, we have to know how to do harder 3 unit projectiles and shms at 4 unit level...but how much harder, i.e. as i said in the first post, to what extent...." - they're not harder, to any extent.

i stand by what i said: "it's not necessary that you have mastered 3u mechanics in order to do 4u mechanics (ext. 2 is just an extension of 3u, it doesn't necessarily mean the topics are harder)"
i'm sure many ppl out there feel the same - that 4u is not necessarily harder than 3u in certain topics.

Edit: the word "EXTENSION" does not carry the connotation of "HARDER" - otherwise why not just call Extension 2 "Harder 3u and 2u mathematics"? "extension 2" topics are ones which are simply those not taught at the "extension 1" level, but are still related due to the scope and breadth of the theories in 3u... so it does not automatically imply, by virtue of definition, increased hardness (which, btw, is a subjective quality.)...

 

[Abtari]

if you take a look at page 56 of the extension 2 syllabus, that should solve all your worries.

 

[who_loves_maths]

if you take a look at page 56 of the extension 2 syllabus, that should solve all your worries

lol, i have no worries with 4u maths.

and i don't spend time reading through the syllabus, i use that time learning the actual content of the course. maybe doing that would solve all YOUR worries...

 

[Abtari]

im glad you're such an efficient student. good for you. thanks for the discussion anyway.

 

[shafqat]

2 and 3 u motion topics are examined in 4u. Whether it's actually harder is a matter of debate. Most 3u questions in 4u exams, while not involving extra theory, are usually more difficult than if they had been in a 3u exam in the same context.

 

[who_loves_maths]

Originally Posted by shafqat
Most 3u questions in 4u exams, while not involving extra theory, are usually more difficult than if they had been in a 3u exam in the same context.

i agree. however, like i said in a previous post here: "... so it does not automatically imply, by virtue of definition, increased hardness (which, btw, is a subjective quality)..." - ie. it's up to the opinions of each individual doing the subject.
however, like i said, i agree that "USUALLY" it is more difficult, but not necessarily.

 

[shafqat]

yes i agree

 

[Abtari]

hey guys,

something concrete and not syllabussy. a question i am having trouble with. arnold book ex 7.2 4b.

A particle of mass m falls from rest under gravity and the resistance to its motion is mkv^2, where v is its speed and k is a positive constant.
a) show that v^2 =g/k(1 - e^-2kx), where x is the distance fallen.
b) As the distance it has fallen increases from d1 to 2d1, the speed increases from v1 to 5/4v1. express the greatest possible speed of the particle in terms of v1.

i had no idea how to APPROACH the b part.

thanks in advance.

 

[justchillin]

from part (a): v1^2=g/k(1-e^-2k(2d1))...
rearraging u get: e^-2k(2d1)=(1-v1^2(k/g))^2
Now subbing in e^-2k(2d1) = (1/v1^2(k/g))^2; into (5/4v1)^2=g/k(1-e^-2k(2d1)) you get...
(5/4v1)^2.k/g=1-(1-v1^2(k/g))^2, rearranging... k/g=7/16.(1/v1^2)
As the restistance to the particle's motion is mkv^2, the greatest possible speed of the particle is v= sqrt(g/k) (ie when mg=mkv^2). But k/g=7/16.(1/v1^2), therefore v=4v1/sqrt(7).
Hope that clears it up for u...