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Boushra
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The following diagram demonstrates an elastic collision between two balls of equal masses. The black ball is at rest and the final velocity v1 of the white ball = 3 m/s Find:
1. the initial velocity of the white ball,
2. the velocity of the black ball after the collision
3. the angle (theta)
4. the change in the kinetic energy
Is there a possibility we can discuss everything here? I'm having a hard time understanding. please help!
 2 years ago
 2 years ago
Boushra Group Title
The following diagram demonstrates an elastic collision between two balls of equal masses. The black ball is at rest and the final velocity v1 of the white ball = 3 m/s Find: 1. the initial velocity of the white ball, 2. the velocity of the black ball after the collision 3. the angle (theta) 4. the change in the kinetic energy Is there a possibility we can discuss everything here? I'm having a hard time understanding. please help!
 2 years ago
 2 years ago

This Question is Closed

Boushra Group TitleBest ResponseYou've already chosen the best response.1
We should use the perfect inelastic collision equation m1u1 + m2u2 = (m1+m2)v
 2 years ago

Vaidehi09 Group TitleBest ResponseYou've already chosen the best response.2
can u post the diagram as well?
 2 years ago

Boushra Group TitleBest ResponseYou've already chosen the best response.1
yep just a sec
 2 years ago

meera_yadav Group TitleBest ResponseYou've already chosen the best response.0
hii, is the black bal at rest after the collision? if yes then white ball's initial velocity is zero just before collision
 2 years ago

Boushra Group TitleBest ResponseYou've already chosen the best response.1
dw:1341315928417:dw
 2 years ago

Boushra Group TitleBest ResponseYou've already chosen the best response.1
the black ball is in motion after collision
 2 years ago

Vaidehi09 Group TitleBest ResponseYou've already chosen the best response.2
then first of all, we can't use the eq u posted abv since the 2 bodies are not sticking together after collision.
 2 years ago

Boushra Group TitleBest ResponseYou've already chosen the best response.1
oh... yeah right @Vaidehi09
 2 years ago

Boushra Group TitleBest ResponseYou've already chosen the best response.1
should we use m1u1+m2u2 = m1v1 + m2v2 ??
 2 years ago

Boushra Group TitleBest ResponseYou've already chosen the best response.1
m1 = m2 = m
 2 years ago

meera_yadav Group TitleBest ResponseYou've already chosen the best response.0
dw:1341316215450:dw
 2 years ago

Boushra Group TitleBest ResponseYou've already chosen the best response.1
should we write an equation based on components?
 2 years ago

meera_yadav Group TitleBest ResponseYou've already chosen the best response.0
since this is an elastic collision then we must have momentum before collision = momentum after collision !! we must also have change in kinetic energy energy should be zero as there's no external force acting..
 2 years ago

Boushra Group TitleBest ResponseYou've already chosen the best response.1
yes understood :) then
 2 years ago

meera_yadav Group TitleBest ResponseYou've already chosen the best response.0
yep ! we should write moemtum shold be resolved.. i.e. horizontal momentum before collison = horizontal momentum after collision same goes for vertical momentum
 2 years ago

meera_yadav Group TitleBest ResponseYou've already chosen the best response.0
similar equation we can write it for vertical momentum also !
 2 years ago

Boushra Group TitleBest ResponseYou've already chosen the best response.1
so the first one you drew above is for the horizontal momentum?
 2 years ago

meera_yadav Group TitleBest ResponseYou've already chosen the best response.0
dw:1341316752653:dw
 2 years ago

meera_yadav Group TitleBest ResponseYou've already chosen the best response.0
yep ! it's for horizontal... 2nd draw is for vertical momentum..
 2 years ago

Vaidehi09 Group TitleBest ResponseYou've already chosen the best response.2
@meera_yadav ur first drawing....shouldn't we have vcos(theta) there...instead of sine?
 2 years ago

Boushra Group TitleBest ResponseYou've already chosen the best response.1
for the first drawing: why did you write down sin theta v, shouldn't it be cos theta v? since we're talking about the horizontal? @meera_yadav
 2 years ago

Vaidehi09 Group TitleBest ResponseYou've already chosen the best response.2
the eq for horizontal should be u1 = 3cos45 + vcosA
 2 years ago

Vaidehi09 Group TitleBest ResponseYou've already chosen the best response.2
supposing theta = A
 2 years ago

Boushra Group TitleBest ResponseYou've already chosen the best response.1
yes, that's what I got @Vaidehi09
 2 years ago

meera_yadav Group TitleBest ResponseYou've already chosen the best response.0
yeah! sorry ! that's a mistake ... thanks for pointing out :) plz correct it to cos theta
 2 years ago

Boushra Group TitleBest ResponseYou've already chosen the best response.1
great!!! now we can move on to 2nd equation:
 2 years ago

Boushra Group TitleBest ResponseYou've already chosen the best response.1
.5 mu (squared) = .5 m 3(squared) + .5 m v(squared) < why did we use this?
 2 years ago

Vaidehi09 Group TitleBest ResponseYou've already chosen the best response.2
wait a sec, but we haven't yet found the value of u1.
 2 years ago

Vaidehi09 Group TitleBest ResponseYou've already chosen the best response.2
thats the eq for conservation of KE
 2 years ago

Boushra Group TitleBest ResponseYou've already chosen the best response.1
yeah, I know,... should we label it as eq 2?
 2 years ago

Vaidehi09 Group TitleBest ResponseYou've already chosen the best response.2
for KE, i got the eq as (u1)^2 = 3^2 + v^2
 2 years ago

Boushra Group TitleBest ResponseYou've already chosen the best response.1
I think the v in it should be v subscript x, correct?
 2 years ago

Vaidehi09 Group TitleBest ResponseYou've already chosen the best response.2
i don't think so. for KE, we don't need components since it is a scalar.
 2 years ago

meera_yadav Group TitleBest ResponseYou've already chosen the best response.0
no there's no need for the subscript vaidelhi , because K.E is a scalar quantity...
 2 years ago

Boushra Group TitleBest ResponseYou've already chosen the best response.1
ok, great, I'm following.. so what do we need next.
 2 years ago

meera_yadav Group TitleBest ResponseYou've already chosen the best response.0
I think everythings known to u know !!
 2 years ago

Vaidehi09 Group TitleBest ResponseYou've already chosen the best response.2
we have another eq, using vertical components for momentum. and that is, vsin theta = 3sin45
 2 years ago

Boushra Group TitleBest ResponseYou've already chosen the best response.1
ok, hold on a sec
 2 years ago

Boushra Group TitleBest ResponseYou've already chosen the best response.1
shouldn't it be 3 sin 45 =  v sin theta?
 2 years ago

Boushra Group TitleBest ResponseYou've already chosen the best response.1
we have it as: 0 = m(3 sin 45) + m (v sin theta) before right?
 2 years ago

Vaidehi09 Group TitleBest ResponseYou've already chosen the best response.2
nope. both the vertical components of velocities are in opp direcs. so we get, 0 = 3sin45  vcosA
 2 years ago

Boushra Group TitleBest ResponseYou've already chosen the best response.1
u mean v sin A ??
 2 years ago

Vaidehi09 Group TitleBest ResponseYou've already chosen the best response.2
ah yes....that should be sine
 2 years ago

Boushra Group TitleBest ResponseYou've already chosen the best response.1
so all I need to do is substitute now? with the 3 eq that I've got?
 2 years ago

Vaidehi09 Group TitleBest ResponseYou've already chosen the best response.2
yup...try it out. m also doing the same.
 2 years ago

Boushra Group TitleBest ResponseYou've already chosen the best response.1
ok, I'll put my answers down.. let's do that :)
 2 years ago

Boushra Group TitleBest ResponseYou've already chosen the best response.1
do we substitue eq 3 into 1?
 2 years ago

Boushra Group TitleBest ResponseYou've already chosen the best response.1
we need to solve for u1 first, right?
 2 years ago

Vaidehi09 Group TitleBest ResponseYou've already chosen the best response.2
i don't know ur numbering. here our the 3 eqs: 1) u = 3cos45 + vcosA 2) u^2 = 9+ v^2 3) vsinA = 3 sin45
 2 years ago

Vaidehi09 Group TitleBest ResponseYou've already chosen the best response.2
our unknowns are u, v, A. start anywhere.
 2 years ago

Boushra Group TitleBest ResponseYou've already chosen the best response.1
let's start with u
 2 years ago

Boushra Group TitleBest ResponseYou've already chosen the best response.1
we should substitute eq 2 into 1?
 2 years ago

Vaidehi09 Group TitleBest ResponseYou've already chosen the best response.2
yea, u can do that or vice versa. whichever is convenient to u.
 2 years ago

Boushra Group TitleBest ResponseYou've already chosen the best response.1
and the take the square root of it first?
 2 years ago

Vaidehi09 Group TitleBest ResponseYou've already chosen the best response.2
that way u can get rid of u.
 2 years ago

Boushra Group TitleBest ResponseYou've already chosen the best response.1
do we go like this: 3 + v = 3 cos 45 + v cos A ??
 2 years ago

Vaidehi09 Group TitleBest ResponseYou've already chosen the best response.2
how did u get 3 + v ?
 2 years ago

Boushra Group TitleBest ResponseYou've already chosen the best response.1
u^2 = 9 + v^2
 2 years ago

Boushra Group TitleBest ResponseYou've already chosen the best response.1
I took the square root of that
 2 years ago

Vaidehi09 Group TitleBest ResponseYou've already chosen the best response.2
u need sqrt( 9+v^2 )
 2 years ago

Vaidehi09 Group TitleBest ResponseYou've already chosen the best response.2
no wait....sqrt( a^2 + b^2) is NOT = a + b
 2 years ago

Boushra Group TitleBest ResponseYou've already chosen the best response.1
can you tell me the way you'd solve for the unknowns from the 3 eq we've got, step by step?
 2 years ago

Vaidehi09 Group TitleBest ResponseYou've already chosen the best response.2
before that, let me confirm something. is the angle theta = 45 ?
 2 years ago

Boushra Group TitleBest ResponseYou've already chosen the best response.1
no, there are two angles, one is theta and one is 45. different from one another. you can refer back to the diagram above
 2 years ago

Vaidehi09 Group TitleBest ResponseYou've already chosen the best response.2
no i mean, do u have the answers?
 2 years ago

Boushra Group TitleBest ResponseYou've already chosen the best response.1
oh yes, it's correct
 2 years ago

Vaidehi09 Group TitleBest ResponseYou've already chosen the best response.2
great...so i'm on the right path. ok proceed this way...
 2 years ago

Boushra Group TitleBest ResponseYou've already chosen the best response.1
I just need to know the steps, I've having a hard time substituting..
 2 years ago

Vaidehi09 Group TitleBest ResponseYou've already chosen the best response.2
no prob, i'll help.
 2 years ago

Boushra Group TitleBest ResponseYou've already chosen the best response.1
can we start by knowing how to substitute and figure out theta?
 2 years ago

Vaidehi09 Group TitleBest ResponseYou've already chosen the best response.2
first, swap ur RHS and LHS of eq 3 and add it to eq 1.
 2 years ago

Boushra Group TitleBest ResponseYou've already chosen the best response.1
what is RHS and LHS?
 2 years ago

Vaidehi09 Group TitleBest ResponseYou've already chosen the best response.2
right hand side and left hand side of an eq.
 2 years ago

Boushra Group TitleBest ResponseYou've already chosen the best response.1
ok, I'd swap them and add them to the 1st equation
 2 years ago

Vaidehi09 Group TitleBest ResponseYou've already chosen the best response.2
so ur eq 3 becomes: 3sin45 = vsinA
 2 years ago

Vaidehi09 Group TitleBest ResponseYou've already chosen the best response.2
right. sow rite down what u got here.
 2 years ago

Vaidehi09 Group TitleBest ResponseYou've already chosen the best response.2
so u should have now, u + 3sin45 = 3cos45 + vcosA + vsinA
 2 years ago

Boushra Group TitleBest ResponseYou've already chosen the best response.1
yes! i got that too
 2 years ago

Vaidehi09 Group TitleBest ResponseYou've already chosen the best response.2
cancel out 3sin45 and 3cos45. so now u have, u = v( cosA + sinA)
 2 years ago

Boushra Group TitleBest ResponseYou've already chosen the best response.1
is there a trig rule for cancelling them out that i should know of?
 2 years ago

Vaidehi09 Group TitleBest ResponseYou've already chosen the best response.2
what is sin45?
 2 years ago

Boushra Group TitleBest ResponseYou've already chosen the best response.1
0.707106 which is the same is cos 45
 2 years ago

Boushra Group TitleBest ResponseYou've already chosen the best response.1
so that's how we cancel them out.. ok!
 2 years ago

Vaidehi09 Group TitleBest ResponseYou've already chosen the best response.2
right...so mathematically, those 2 terms are exactly the same. and on opp sides of the = sign. so we can cancel them out.
 2 years ago

Vaidehi09 Group TitleBest ResponseYou've already chosen the best response.2
ok, moving on...substitute that eq in eq2.
 2 years ago

Boushra Group TitleBest ResponseYou've already chosen the best response.1
perfect, now we're left with u = v ( cos A + sin A)
 2 years ago

Vaidehi09 Group TitleBest ResponseYou've already chosen the best response.2
u should get : v^2(sinA+cosA)^2 = 9+ v^2
 2 years ago

Boushra Group TitleBest ResponseYou've already chosen the best response.1
do we get: (v(cos A + sin A) ^2 = 9 + v^2 ?
 2 years ago

Boushra Group TitleBest ResponseYou've already chosen the best response.1
yep, the same.
 2 years ago

Vaidehi09 Group TitleBest ResponseYou've already chosen the best response.2
that's right, now expand LHS and show me what u get.
 2 years ago

Boushra Group TitleBest ResponseYou've already chosen the best response.1
i think there' a rule saying cos A + sin A = 1?
 2 years ago

Vaidehi09 Group TitleBest ResponseYou've already chosen the best response.2
no...that's when cosA and sinA both are squared terms
 2 years ago

Boushra Group TitleBest ResponseYou've already chosen the best response.1
ok, then hold a sec
 2 years ago

Boushra Group TitleBest ResponseYou've already chosen the best response.1
should we get v^2cos^2A +sin^2A = 9 + v^2 ??
 2 years ago

Vaidehi09 Group TitleBest ResponseYou've already chosen the best response.2
do u know the expansion of (a+b)^2 ?
 2 years ago

Boushra Group TitleBest ResponseYou've already chosen the best response.1
yes... oh wait, I made a mistake.. just a sec
 2 years ago

Boushra Group TitleBest ResponseYou've already chosen the best response.1
v^2 sin^2a + 2sinAcosA + cos^2 a = 9 + v^2
 2 years ago

Vaidehi09 Group TitleBest ResponseYou've already chosen the best response.2
thats right, except that, the trigo terms should be inside the bracket and v^2 outside it.
 2 years ago

Boushra Group TitleBest ResponseYou've already chosen the best response.1
ok so : v^2 (sin^2a + 2sinAcosA + cos^2 a) = 9 + v^2
 2 years ago

Boushra Group TitleBest ResponseYou've already chosen the best response.1
and then...
 2 years ago

Vaidehi09 Group TitleBest ResponseYou've already chosen the best response.2
right, now sin^2a + cos^2a = 1 so we get v^2( 1 + sin2a) = 9 + v^2 v^2 + v^2sin2a = 9 + v^2 v^2sin2a = 9
 2 years ago

Vaidehi09 Group TitleBest ResponseYou've already chosen the best response.2
sin2a = 2sinacosa...thats the sub i made.
 2 years ago

Boushra Group TitleBest ResponseYou've already chosen the best response.1
wiat.. shouldn't we habe v^2 (1 + 2sinAcosA) = 9 + v^2 ??
 2 years ago

Vaidehi09 Group TitleBest ResponseYou've already chosen the best response.2
look at the second last post. i showed how I substituted.
 2 years ago

Vaidehi09 Group TitleBest ResponseYou've already chosen the best response.2
there's a formula : sin2A = 2sinAcosA. i used it.
 2 years ago

Boushra Group TitleBest ResponseYou've already chosen the best response.1
aha... ok, got it.. and now what's next?
 2 years ago

Boushra Group TitleBest ResponseYou've already chosen the best response.1
so the final formula here is v^2 sin2 a = 9
 2 years ago

Vaidehi09 Group TitleBest ResponseYou've already chosen the best response.2
now divide the eq which we got hen, by eq 3. so \[v ^{2} \sin2A / vsinA = 9/\3sin45\] so we'll get vsinAcosA/sinA = 9 sqrt(2)/3.......since 3sin45 = 3/sqrt(2)
 2 years ago

Vaidehi09 Group TitleBest ResponseYou've already chosen the best response.2
in the eq, the RHS is 9/3sin45
 2 years ago

Boushra Group TitleBest ResponseYou've already chosen the best response.1
ok, the RHS is 9/3 sin 45 = 4.2426 ???
 2 years ago

Vaidehi09 Group TitleBest ResponseYou've already chosen the best response.2
don't go on to the final values just yet. it'll only complicate things further.
 2 years ago

Vaidehi09 Group TitleBest ResponseYou've already chosen the best response.2
continuing the above eq, we'll gte vcosA = 3 sqrt(2)
 2 years ago

Vaidehi09 Group TitleBest ResponseYou've already chosen the best response.2
gr8! so now divide this eq with ur eq3
 2 years ago

Vaidehi09 Group TitleBest ResponseYou've already chosen the best response.2
u should get vcosA/vsinA = 3 rt(2)/ [3/rt(2)]
 2 years ago

Boushra Group TitleBest ResponseYou've already chosen the best response.1
yes that's what i got
 2 years ago

Vaidehi09 Group TitleBest ResponseYou've already chosen the best response.2
which would lead us to cotA = 2 or tanA = 1/2
 2 years ago

Vaidehi09 Group TitleBest ResponseYou've already chosen the best response.2
so now u can find A = tan^(1) [1/2]
 2 years ago

Boushra Group TitleBest ResponseYou've already chosen the best response.1
wait cos a/sina = tan a?
 2 years ago

Vaidehi09 Group TitleBest ResponseYou've already chosen the best response.2
no, cosa /sina = cota = 1/tana
 2 years ago

Boushra Group TitleBest ResponseYou've already chosen the best response.1
what's cota?
 2 years ago

Boushra Group TitleBest ResponseYou've already chosen the best response.1
yeah, i mean what's cot?
 2 years ago

Vaidehi09 Group TitleBest ResponseYou've already chosen the best response.2
u dont know ur trigo ratios?
 2 years ago

Boushra Group TitleBest ResponseYou've already chosen the best response.1
this is the first time I see cot, I will definitely look up all the ratios after this
 2 years ago

Vaidehi09 Group TitleBest ResponseYou've already chosen the best response.2
no wait..before solving such questions, u should go and work on ur math. u've reached mechanics, u ought to have a solid base in math for it.
 2 years ago

Boushra Group TitleBest ResponseYou've already chosen the best response.1
so what do i need to look up in regards to trig in mechanics?
 2 years ago

Vaidehi09 Group TitleBest ResponseYou've already chosen the best response.2
trigo ratios are elementary in trigo. u need to know the various relations between them. their values for basic angles. formulae etc etc.
 2 years ago

Vaidehi09 Group TitleBest ResponseYou've already chosen the best response.2
and then there will come inverse trigo ratios...something that we were going to use here, to find out theta.
 2 years ago

Boushra Group TitleBest ResponseYou've already chosen the best response.1
alright then, nonetheless... i really really really appreciate your help. I will go look those basics up first, and then perhaps come back and solve the question here. Thank you soooo very much :)
 2 years ago

Boushra Group TitleBest ResponseYou've already chosen the best response.1
yeah i know inverse ratios :)
 2 years ago

Vaidehi09 Group TitleBest ResponseYou've already chosen the best response.2
cool! and considering how much we've solved here, u should be able to go further without any external help. work hard on math! don't ignore it!
 2 years ago

Vaidehi09 Group TitleBest ResponseYou've already chosen the best response.2
@Boushra: I had made a calculation error before. after getting v^2sin2A/vsinA = 9/[3/sqrt(2)] we'll get, 2vcosA = 3 rt(2) therefore, vcosA = 3/rt(2) comparing this with eq3, ie., vsinA = 3/rt(2) we can conclude thata cosA = sinA therefore A = 45
 2 years ago

Vaidehi09 Group TitleBest ResponseYou've already chosen the best response.2
so after substituting u'll get v = 3m/s u = 3 rt(2) m/s and A = theta = we already got as 45
 2 years ago
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