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 2 years ago
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
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!

This Question is Closed

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

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

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

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

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

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

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

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

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

meera_yadav
 2 years ago
Best ResponseYou've already chosen the best response.0since 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..

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

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

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

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

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

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

Boushra
 2 years ago
Best ResponseYou've already chosen the best response.1for 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

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

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

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

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

Boushra
 2 years ago
Best ResponseYou've already chosen the best response.1.5 mu (squared) = .5 m 3(squared) + .5 m v(squared) < why did we use this?

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Boushra
 2 years ago
Best ResponseYou've already chosen the best response.10.707106 which is the same is cos 45

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Vaidehi09
 2 years ago
Best ResponseYou've already chosen the best response.2right, 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

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

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

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

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

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

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

Vaidehi09
 2 years ago
Best ResponseYou've already chosen the best response.2now 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)

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

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

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

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

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

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

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

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

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

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

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

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

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

Vaidehi09
 2 years ago
Best ResponseYou've already chosen the best response.2no 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.

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

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

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

Boushra
 2 years ago
Best ResponseYou've already chosen the best response.1alright 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 :)

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

Vaidehi09
 2 years ago
Best ResponseYou've already chosen the best response.2cool! 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!

Vaidehi09
 2 years ago
Best 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

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