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Mega A Level Maths Thread MK II

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Thanks and to be honest I can't really get anywhere with DJ's question as I'm not too confident in proving things in Mechanics :-/

Well, first of all think back to basics. If you have a constant force acting on the body, what does this imply? Does this provide any hints on other things you could potentially use?

More explicit hint:

Spoiler

Reply 2401

joostan

Original post by DJMayes

Prove that, if a constant force acts on a body, then the work done by the force is equal to the change in kinetic energy of the body.

No peeking MathsNerd :tongue:

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(edited 10 years ago)

Reply 2402

Scientific Eye

Original post by joostan

No peeking MathsNerd :tongue:

Spoiler

Reply 2403

MathsNerd1

Original post by DJMayes

Spoiler

Well I know what the equation will be for change in KE is 1/2*m(V^2-U^2) and if you have a constant force acting upon something then you'll have your resultant force equation with a constant acceleration. I'm guessing some rearrangement of this will get me the answer?

(edited 10 years ago)

Reply 2404

justinawe

Original post by MathsNerd1

Hmm, I'm not sure with that as I'm not too strong in the Mechanics section but I'd probably start by drawing a diagram and going from there?

I haven't really done much mechanics, but I'm pretty sure no diagrams are involved.

I tried doing a calculus proof, but got nowhere so I gave up and cheaply used SUVAT :teehee:

Reply 2405

justinawe

Original post by joostan

No peeking MathsNerd :tongue:

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Reply 2406

joostan

Original post by Scientific Eye

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Original post by justinawe

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Reply 2407

justinawe

Original post by joostan

Spoiler

u=0 was not a condition though :colone:

and it's supposed to be change in K.E., so I'm not sure if your proof covers all the bases :sly:

Reply 2408

joostan

Original post by justinawe

u=0 was not a condition though :colone:

and it's supposed to be change in K.E., so I'm not sure if your proof covers all the bases :sly:

Are you happy now? I edited it in :tongue:

I've not done M2 I was going for the physics KE equation :redface:

Reply 2409

justinawe

Original post by joostan

Are you happy now? I edited it in :tongue:

I've not done M2 I was going for the physics KE equation :redface:

I haven't even done M1, so that's not an excuse! :noway:

Reply 2410

joostan

Original post by justinawe

I haven't even done M1, so that's not an excuse! :noway:

Original post by DJMayes

Hehe:
OK . . .Calculus proof:

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(edited 10 years ago)

Reply 2411

justinawe

Original post by joostan

Hehe:
OK . . .Calculus proof:

Spoiler

Yeah, did that too :tongue:

I was trying something else out of curiosity to see if it worked :colone:

Reply 2412

joostan

Original post by justinawe

Yeah, did that too :tongue:

I was trying something else out of curiosity to see if it worked :colone:

Yeah I played around with:

a = \dfrac{d^2x}{dt^2}

but nothing seemed to come of it :smile:

Reply 2413

justinawe

Original post by joostan

Yeah I played around with:

a = \dfrac{d^2x}{dt^2}

but nothing seemed to come of it :smile:

This is probably utter nonsense, but:

W = \displaystyle \int F \ dx

\Rightarrow W = \displaystyle \int \frac{dp}{dt} \ dx

\Rightarrow W = \displaystyle \int \frac{dx}{dt} \ dp

\Rightarrow W = \displaystyle \int v \ dp

integrating p wrt v apparently gives K.E., but "wrt v" is pretty meaningless I think... but anyway, I got something slightly different :redface:

Reply 2414

GCSE-help

For C2, a lot of things need so much 'mathematical imagination'. How do people deal with these situations? Like when sometimes you just have to 'know' to use SOHCAHTOA, sometimes you have to know to use a circle theorem etc etc

Reply 2415

joostan

Original post by justinawe

This is probably utter nonsense, but:

W = \displaystyle \int F \ dx

\Rightarrow W = \displaystyle \int \frac{dp}{dt} \ dx

\Rightarrow W = \displaystyle \int \frac{dx}{dt} \ dp

\Rightarrow W = \displaystyle \int v \ dp

integrating p wrt v apparently gives K.E., but "wrt v" is pretty meaningless I think... but anyway, I got something slightly different :redface:

That works out quite nicely if you say that:

v = \frac{1}{m}p

Original post by GCSE-help

I'm not sure that knowing SOHCAHTOA is mathematical imagination, it's just expected knowledge I guess.

(edited 10 years ago)

Reply 2416

justinawe

Original post by joostan

That works out quite nicely if you say that:

v = \frac{1}{m}p

Oh, right, thanks for that :colone:

Reply 2417

Scientific Eye

Original post by GCSE-help

Having experience really helps. So, the more you practise with these types of questions, the more you develop your intuition as to when you need to use those mathematical tools.