VCE Specialist 3/4 Question Thread!

[BubbleWrapMan]

Well , so you're going through the whole circle (almost). Hence you shouldn't discard the negative.

[duhherro]

Well , so you're going through the whole circle (almost). Hence you shouldn't discard the negative.

Ahh  yeah, good point, this question is structured differently in that you have to work out both pos and neg value haha!


Thanks again ! Although still a bit confused on the 9c) linearly dependent one T_T

[barydos]

Just checking, with a vector function r(t), are the values of v(0) and a(0) open circle on a graph, since r(t) not differentiable at x=0???

And as quoted from Re: Specialist Mathematics Resources :

Spoiler

●  CONVEYOR BELT QUESTIONS EXPLAINED
~ Friction used to pull object. So in this special case, friction is in the direction of motion.

~ can have a value bigger than 1

~ Belt can accelerate faster than object on belt. When this happens the object slips down the belt because of its negative relative acceleration, yet it still has a positive acceleration relative to the ground.

~ Object has maximum acceleration determined by coefficient of friction of belt. Cannot exceed this acceleration, and if belt exceed this, object still remain at maximum acceleration

do I need to know this?
I don't think I've ever done a question on conveyor belts before o.o

[lzxnl]

Yay conveyor belts. I've never seen those questions in spesh; I've seen them in uni physics though.

Technically, you're right about the initial values of v and a; they strictly speaking aren't defined. They can't take a mark off I guess for leaving them out.

[Stevensmay]

Just checking, with a vector function r(t), are the values of v(0) and a(0) open circle on a graph, since r(t) not differentiable at x=0???

And as quoted from Re: Specialist Mathematics Resources :

Spoiler

●  CONVEYOR BELT QUESTIONS EXPLAINED
~ Friction used to pull object. So in this special case, friction is in the direction of motion.

~ can have a value bigger than 1

~ Belt can accelerate faster than object on belt. When this happens the object slips down the belt because of its negative relative acceleration, yet it still has a positive acceleration relative to the ground.

~ Object has maximum acceleration determined by coefficient of friction of belt. Cannot exceed this acceleration, and if belt exceed this, object still remain at maximum acceleration

do I need to know this?
I don't think I've ever done a question on conveyor belts before o.o

Was speaking to b^3 about these earlier. Apparently no longer on the course.

[Alwin]

Was speaking to b^3 about these earlier. Apparently no longer on the course.

yup. I think I've only seen them in very old checkpoints, maybe 2003 or 2004 it was.


Also, just a little thing when drawing vector paths on a Cartesian plane, do we HAVE to draw a little arrow indicating what direction the particle is travelling?

[brightsky]

1. contentious point. technically the particle does have an initial velocity and acceleration. think about what happens in real life. if they ask for an initial velocity and/or acceleration, then obviously you will have to include the 0.

2. conveyor belts aren't mentioned in the study design but best to know just to be safe. apply your principles. think about the scenario in real life.

i) if you were brick sitting on top of a conveyor belt, what would be the forces acting on you? you have a weight force, for obvious reasons, and normal force, which the conveyor belt exerts onto you in order to stop you from falling through it. but obviously if you are moving with the conveyor belt, there must be a force acting in the forward direction. what is this force? is it a tension force? no ropes. is it thrust? no a brick has no thrust. the brick is moving because of the friction that exists between it and the conveyor belt. if the conveyor belt were coated with a layer of oil, then the brick probably just stay where it is. so the friction force must be causing the object to move in the forward direction.

ii) just a fun fact, which you may or may not need to know. I've never seen a vcaa question, or a question from any other company, which features a slope with a friction greater than 1 though. but if you do see a question which has that kind of slope, then work with it. no dramas.

iii) the conveyor belt can move at the speed of light. now obviously, unless the coefficient of friction between the brick and the conveyor belt is infinity, you can't be moving with the conveyor belt if the conveyor belt is moving at the speed of light. you will most likely slip. think about what happens when the conveyor belt first begins to move. the friction force which is pulling you in the forward direction increases from 0, slowly and gradually. as the conveyor belt moves faster, the friction force increases more and more. you will eventually reach a point where the friction force reaches an absolute maximum and cannot increase any more. the value of the maximum friction force equals to uN, as you know. when this occurs the brick is on the point of slipping backwards. if you increase the conveyor belt even more, the brick will actually slip and it will maintain its acceleration no matter how much more you increase the speed of the conveyor belt. (note that the brick will likely still be moving in the forward direction relative to a stationary onlooker, but slipping backwards relative to the conveyor belt, if you get what I mean.) note that it is only when the brick is on the point of slipping, or actually slipping, that the friction force acting in the forward direction equals uN. common trap.

iv) dealt with above.

hope this makes sense.

[brightsky]

yup. I think I've only seen them in very old checkpoints, maybe 2003 or 2004 it was.


Also, just a little thing when drawing vector paths on a Cartesian plane, do we HAVE to draw a little arrow indicating what direction the particle is travelling?

no. can be difficult sometimes especially when the object moves back and forth along the same curve. but if you can, do, just to be safe.

[barydos]

Thanks guys, especially brightsky awesome explanation I get it now cheers

Another question: http://www.vcaa.vic.edu.au/Documents/exams/mathematics/2007specmaths1.pdf
For question 8b: when doing the arctan(-1), do we choose in preference to because (0,-1) is between quadrants 3 and 4? Or is there another explanation for this?

[Alwin]

Thanks guys, especially brightsky awesome explanation I get it now cheers

Another question: http://www.vcaa.vic.edu.au/Documents/exams/mathematics/2007specmaths1.pdf
For question 8b: when doing the arctan(-1), do we choose in preference to because (0,-1) is between quadrants 3 and 4? Or is there another explanation for this?

The range of arctan(x) is -pi/2 to pi/2 (remember because of restriction)

So then it cannot be  3pi/4 because this is outside of the range of -pi/2 to pi/2

(or you can think about it in reverse, Tan(x) is only defined for -pi/2 to pi/2 etc etc )

[barydos]

The range of arctan(x) is -pi/2 to pi/2 (remember because of restriction)

So then it cannot be  3pi/4 because this is outside of the range of -pi/2 to pi/2

(or you can think about it in reverse, Tan(x) is only defined for -pi/2 to pi/2 etc etc )

Oh damn thanks, I was thinking of the domain of arctan my bad. Much appreciated

[ahat]

Has any body got some difficult Volumes of Revolution of Complex Number questions (and/or vectors and their calculus)? Need some practice, cheers!

[SocialRhubarb]

Has any body got some difficult Volumes of Revolution of Complex Number questions (and/or vectors and their calculus)? Need some practice, cheers!

[Stevensmay]

Does anyone mind explaining Question 4 part a for me?

http://www.vcaa.vic.edu.au/Documents/exams/mathematics/2012/2012specmath1-w.pdf
http://www.vcaa.vic.edu.au/Documents/exams/mathematics/2012/specmaths1_assessrep12.pdf

Thank you.

[Jeggz]

Can someone please help me out with VCAA 2007 Paper 1 - Q7a) ?
I usually know how to do these questions, but for some reason my answer is not satisfying VCAA's answer :\
Thanks in advance!
http://www.vcaa.vic.edu.au/Documents/exams/mathematics/2007specmaths1.pdf