4U Maths Question Thread

[Mei2016]

Ok, thanks.

[amandali]

i

i dont know how to do part iv) 

[RuiAce]

Hint for the time being:

The question just means to find the normal reaction the surface exerts on the particle.

Remember: According to Newton's Third Law of Motion, the normal reaction the surface exerts on the particle has the same magnitude as the force the particle exerts onto the bowl.

> > > Please do not double post < < <

This was the best I could come up with.

Basically just use a Pythagorean identity.

[massive]

guys quick question:
Find the equation of the normal to the ellipse at P (2cos(theta), sqrt(3)sin(theta)) and prove that it bisects angle SPS' where S and S' are the foci
I can get the normal but i just can't get the second part of the question, thanks for the help!

[RuiAce]

guys quick question:
Find the equation of the normal to the ellipse at P (2cos(theta), sqrt(3)sin(theta)) and prove that it bisects angle SPS' where S and S' are the foci
I can get the normal but i just can't get the second part of the question, thanks for the help!

This is just asking you to prove the reflection property for the ellipse. It'll be in your textbook.

Some questions in past HSC papers (I think there was one in 2009) also made students prove the reflection property. They did it for the hyperbola, though, which tweaks the proof a little.

[massive]

This is just asking you to prove the reflection property for the ellipse. It'll be in your textbook.

Some questions in past HSC papers (I think there was one in 2009) also made students prove the reflection property. They did it for the hyperbola, though, which tweaks the proof a little.

The answers prove that PS/PS' = ST/S'T and therefore the normal bisects angle SPS' :S how does that work?? (BTW T is the x intercept of the normal)

[RuiAce]

The answers prove that PS/PS' = ST/S'T and therefore the normal bisects angle SPS' :S how does that work?? (BTW T is the x intercept of the normal)

Check one of the past papers such as 2009. There's a small proof as to how you can then use similar triangles to induce your required result.

You're required to memorise up to PS/PS' = TS/TS' by yourself. That last bit you'd be told guided to prove separately if you had to.

[katherine123]

need help with these ques:
1.a particle of mass M is attached to one end of a light inelastic string of length `2a and the other end is fastened to a fixed point O on a smooth horizontal table. Another particle also of mass M is attached to the midpoint of the string. The system then rotates in a horizontal circle and in contact with the table at an angular velocity of w. Find the ratio of the tensions in each part of the string.

2.a find of mass 0.6kg is attached to a point P on a string AB of length 1.4m, where AP is 0.8m. The ends A and B are attached to 2 points 1.0m apart in a vertical line, A being above B. THe ring is made to travel in a horizontal circle with speed v m/s.
what is the smallest possible values of v if neither portion of string is slack?

[RuiAce]

need help with these ques:
1.a particle of mass M is attached to one end of a light inelastic string of length `2a and the other end is fastened to a fixed point O on a smooth horizontal table. Another particle also of mass M is attached to the midpoint of the string. The system then rotates in a horizontal circle and in contact with the table at an angular velocity of w. Find the ratio of the tensions in each part of the string.

2.a find of mass 0.6kg is attached to a point P on a string AB of length 1.4m, where AP is 0.8m. The ends A and B are attached to 2 points 1.0m apart in a vertical line, A being above B. THe ring is made to travel in a horizontal circle with speed v m/s.
what is the smallest possible values of v if neither portion of string is slack?

I do not take credit for an answer that's not mine. All credit goes to the person i seek for help. (I honestly could not understand Q2 at all when I first saw it without an appropriate diagram.)

Apparently, the scenario to Q1 is similar to this one.
Again, the HSC would be more explicit about the forces involved.

Try to work through his help. Draw a relevant diagram, and upload anything you have thus far if you're stuck halfway through and I should be able to continue it.

[massive]

yo guys does anybody know what papers contain circular motion questions, I've been looking everywhere and can't seem to find any. thanks!

[RuiAce]

yo guys does anybody know what papers contain circular motion questions, I've been looking everywhere and can't seem to find any. thanks!

That's because the HSC is highly unlikely to ask a question that's bluntly related to circular motion. It's virtually always on one of the applications. of it - conical pendulum or banked tracks.

Why? Because what is there to examine you on.

There may be some trial papers with a few multiple choice on them. Try browsing through THSC.

[massive]

Hey just quickly, do you guys know of any little pointers to remember for mechanics, i think it occurs mostly in conical pendulum. What i mean is for e.g. when N=0 the particle is no longer touching the surface and also if w^2>0 then the particle is moving. Does anybody know anything else to keep an eye out for?

[RuiAce]

Hey just quickly, do you guys know of any little pointers to remember for mechanics, i think it occurs mostly in conical pendulum. What i mean is for e.g. when N=0 the particle is no longer touching the surface and also if w^2>0 then the particle is moving. Does anybody know anything else to keep an eye out for?

0≤θ<π/2 if you do it correctly. (If the angle is 0 then obviously you're at rest though, and that's basically the same thing as saying ω²=0 so you usually don't get that happening.)
You can't have a conical pendulum that goes inverted just by itself.

Maximal tension a string can cope with is something but you're usually guided as to how to approach this type of question.

And of course in general: string means tension, surface means normal reaction (and friction if appropriate - smooth surface implies no friction).

That's basically all off the top of my head I reckon.

[jakesilove]

For anyone looking to absolutely smash their HSC exam, understanding what the question actually expects of you is vital. Check our Rui's beast guide of Maths verbs HERE, and get an edge in your final exam! As always, thanks must go out to the legend himself, RuiAce; Improving Atars Since 2015.

[katherine123]

how to do last part