VCE Specialist 3/4 Question Thread!

[Lasercookie]

Will we ever encounter questions regarding volumes being rotated around a line apart from the x/y axis? e.g. Rotated around x=2 or something?

I don't remember for VCAA exams, but fairly sure a few company exams have had such questions. If it was a horizontal/vertical line, you just translate the function so that you're revolving around the x or y axis anyway.

Looking at the study design now, it states: "• application of integration to finding areas of regions bounded by curves and to volumes of solids of revolution of a region about either coordinate axis." so I guess you can take that as a no for VCAA exams.

[UoM]

In SACs possibly. I had a question about a rotation around an asymptote (that wasn't lying on an axis)

Ehh lol, how do I rotate it around an asymptote? o_O

I don't remember for VCAA exams, but fairly sure a few company exams have had such questions. If it was a horizontal/vertical line, you just translate the function so that you're revolving around the x or y axis anyway.

Looking at the study design now, it states: "• application of integration to finding areas of regions bounded by curves and to volumes of solids of revolution of a region about either coordinate axis." so I guess you can take that as a no for VCAA exams.

I know how to rotate it around constants such as x=2 or y=6 but from the preceeding response, how do I rotate it around an asymptote? O_O
Also, could you please link me to a list of the study designs? I've never really bothered checking VCE related websites hah.

[Lasercookie]

Also, could you please link me to a list of the study designs? I've never really bothered checking VCE related websites hah.

Check the VCAA website and go from there, or the quicker method of just googling '[vce subject name] study design' and find the relevant VCAA link. Study designs will be linked under each subject's 'index page', so just googling the vce subject name should find that too. It's probably time to scour through the VCAA website for the stuff relevant to your subjects (study designs and the past exams pages being the most important). 

[pi]

Ehh lol, how do I rotate it around an asymptote? o_O

eg. a question from aforementioned SAC which I posed as a challenge question to the forum last year

A cissoid (where and ) is rotated about it's asymptote to form a volume of revolution. Find this volume in terms of . You don't really need a CAS until the very last part to get the answer.

So the asymptote is x=2a
Rotate: radius (2a-x)
            height dy



Sub (1) into (2)

[UoM]

Check the VCAA website and go from there, or the quicker method of just googling '[vce subject name] study design' and find the relevant VCAA link. Study designs will be linked under each subject's 'index page', so just googling the vce subject name should find that too. It's probably time to scour through the VCAA website for the stuff relevant to your subjects (study designs and the past exams pages being the most important). 

Cheers mate, you got anything else you'd recommend I should read and bookmark? I never knew VCAA put so much detail into all of their study designs, thought it was just a few sentences hah.
I'm saving the VCAA exams for September holidays though.

eg. a question from aforementioned SAC which I posed as a challenge question to the forum last year

Well, I don't really understand it, but thankfully it's not going to be examined. (Nek mennit...)

Thanks boys, really appreciate the help.

[lzxnl]

I'm going to be very nit picky and say this.
You can't have dy = some function of x without a dx. Otherwise it makes no sense.

[Homer]

Kris wants to move a box of mass 50 kg which is resting on a rough, level floor.
a. If Kris pulls on the box with a horizontal force of 140 N, he can just make the box slide across the floor.
Find the coefficient of friction between the box and the floor.
b. If Kris pulls on the box with a force of P N acting at an angle of 15° to the horizontal, what is the least
value of P that will just make the box slide across the floor? Give your answer correct to the nearest
integer.

Can do a but not b

[SocialRhubarb]

Part A:







Part B:

The vertical component of the force applied will act to counteract the weight force and reduce the normal force. The horizontal component will act to counteract the frictional force.



Then you just need to solve for P.

[lzxnl]

OK, so answer to a is simply 2/7. Call this

Now the component of P that acts vertically is P sin 15. If we resolve the forces going vertically, forces up = forces down,
Friction force hence attains a max value of
The horizontal force component is simply P cos 15
So
Solve.

[Homer]

hey nliu i tried solving your way and i got 114N, the answer says 135N

[Phy124]

hey nliu i tried solving your way and i got 114N, the answer says 135N

So
Solve.

Should be 

[lzxnl]

Yeah my bad.
Quite clearly I can't think after an entire day of UMEP physics labs.

[barydos]

Hi
I'm just struggling with some extended response questions right now.
I'm not able to do part b) of this question:


and part b and afterwards in this question 15:

Spoiler

I was able to do part a... but I'm not sure why you can't just sub in H/2 into H to do question b) :/
the answers for q15 is here:

Spoiler

if anyone could help me, i'd appreciate it

[b^3]

10b. Find an equation for the circle, then try rotating around the axis, restricting the part you rotating by using terminals in terms of

Spoiler

Part a is asking for an expression for the volume if you filled any shape of height H up fully. While part b asks for the volume when you only half fill it up. They are different because in this case half filling a container of this shape that is 10 cm high is not the same as completely filling a container of this shape that is 5 cm high.

What you need to do for part b is similar to the previous problem, set up the volume of revolution integral, but with the lower terminal as zero, and the upper terminal as .

[sin0001]

Part a is asking for an expression for the volume if you filled any shape of height H up fully. While part b asks for the volume when you only half fill it up. They are different because in this case half filling a container of this shape that is 10 cm high is not the same as completely filling a container of this shape that is 5 cm high.

What you need to do for part b is similar to the previous problem, set up the volume of revolution integral, but with the lower terminal as zero, and the upper terminal as .

Can you please help me with 15c), from the same question