VCE Specialist 3/4 Question Thread!

[lzxnl]

Can anyone please clarify what is meant exactly by the image attached ?

Basically, that means when doing separation of variables, if the RHS is zero, you can't divide by it. So when you write dx/dy = 1/(y-2), that's only valid if y isn't 2.

Alternatively, you can solve the differential equation dy/dx = y-2 to get y = A e^x + 2, and the solution y=2 is obtained by setting A=0.

[knightrider]

Basically, that means when doing separation of variables, if the RHS is zero, you can't divide by it. So when you write dx/dy = 1/(y-2), that's only valid if y isn't 2.

Alternatively, you can solve the differential equation dy/dx = y-2 to get y = A e^x + 2, and the solution y=2 is obtained by setting A=0.

Thanks for clarifying lzxnl, and well done on your awesome uni scores 

[knightrider]

For this image attached.

In particular for the definite integral method.

can we write and then preceded as normal ? Does VCAA recognise this notation?

[zsteve]

For this image attached.

In particular for the definite integral method.

can we write and then preceded as normal ? Does VCAA recognise this notation?

That looks good to me, y(x) is good notation imo.

[sweetiepi]

Hi!
Can someone explain the relevance of Torricelli's Water Flow to spesh? I've tried for ~2 hours to understand it and it still doesn't make much sense. TIA!

[knightrider]

Anyone know how to do the attached on the casio classpad?

many thanks 

[Syndicate]

Hey guys,

How would I convert this parametric equation:



Thanks,
Syndicate

[RuiAce]

Hey guys,

How would I convert this parametric equation:



Thanks,
Syndicate

[Syndicate]

Thanks Rui 

[zsteve]

Hey guys,

How would I convert this parametric equation:



Thanks,
Syndicate

I thought I'd add, your parameterisation for (x, y) uses the hyperbolic functions cosh and sinh. If you're bored and want to learn some maths, they're quite interesting to look into!
Here, you've got
x = 2cosh(ln(2)t), y=2sinh(ln(2)t)

[RuiAce]

Yeah.

[Syndicate]

I thought I'd add, your parameterisation for (x, y) uses the hyperbolic functions cosh and sinh. If you're bored and want to learn some maths, they're quite interesting to look into!
Here, you've got
x = 2cosh(ln(2)t), y=2sinh(ln(2)t)

Although I am quite interested to learn more about hyperbolic trig functions (I will certainly ), I just want to confirm whether they are  acceptable to use in specialist? ( so the second solution Rui provided would also be acceptable to use?)

Thanks,
Syndicate

[zsteve]

Although I am quite interested to learn more about hyperbolic trig functions (I will certainly ), I just want to confirm whether they are  acceptable to use in specialist? ( so the second solution Rui provided would also be acceptable to use?)

Thanks,
Syndicate

Uhh lol their use would be questionable in a specialist exam as they aren't in the SD

[Apink!]

Two particles of mass m₁ kg and m₂ kg (m₂ > m₁) are connected by a light inextensible string that passes over a small pulley and then released.

The equation of motion for the mass m1

B. m₁a = m₁g - T (what I said)

E. m₁a = T- m₁g  (the answer)

Can someone tell me where I went wrong. I attach a dodgy diagram that's in the question that I drew

EDIT: I have another question. I know that friction is F max = uN when object is moving or "on the verge of moving". How do you figure out if an object is on the verge of moving? Does the question tell you that? Usually it just says "is at rest" or "is moving..." But I've never come across "is on the verge of moving". If an object is at rest BUT is on a slanted slide, would you classify that as on the verge of moving?

[lzxnl]

Two particles of mass m₁ kg and m₂ kg (m₂ > m₁) are connected by a light inextensible string that passes over a small pulley and then released.

The equation of motion for the mass m1

B. m₁a = m₁g - T (what I said)

E. m₁a = T- m₁g  (the answer)

Can someone tell me where I went wrong. I attach a dodgy diagram that's in the question that I drew

EDIT: I have another question. I know that friction is F max = uN when object is moving or "on the verge of moving". How do you figure out if an object is on the verge of moving? Does the question tell you that? Usually it just says "is at rest" or "is moving..." But I've never come across "is on the verge of moving". If an object is at rest BUT is on a slanted slide, would you classify that as on the verge of moving?

Well if m2>m1, the m2 mass is moving down and the m1 mass is moving up. This means that the tension force must be greater than m1g.

As for friction, F = uN when it's moving, but the coefficient of friction is a coefficient of kinetic friction, whereas Fmax = uN for verge of moving has a coefficient of static friction; the former is generally smaller than the latter. If something is on the verge of moving, they WILL tell you. Something at rest on a slanted slide isn't on the verge of moving though; the friction force then might not be at its maximum.