Got Homework?
Connect with other students for help. It's a free community.
Here's the question you clicked on:
 0 viewing
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!
 one year ago
 one year 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!
 one year ago
 one year ago

This Question is Closed

BoushraBest ResponseYou've already chosen the best response.1
We should use the perfect inelastic collision equation m1u1 + m2u2 = (m1+m2)v
 one year ago

Vaidehi09Best ResponseYou've already chosen the best response.2
can u post the diagram as well?
 one year ago

meera_yadavBest 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
 one year ago

BoushraBest ResponseYou've already chosen the best response.1
the black ball is in motion after collision
 one year ago

Vaidehi09Best 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.
 one year ago

BoushraBest ResponseYou've already chosen the best response.1
oh... yeah right @Vaidehi09
 one year ago

BoushraBest ResponseYou've already chosen the best response.1
should we use m1u1+m2u2 = m1v1 + m2v2 ??
 one year ago

meera_yadavBest ResponseYou've already chosen the best response.0
dw:1341316215450:dw
 one year ago

BoushraBest ResponseYou've already chosen the best response.1
should we write an equation based on components?
 one year ago

meera_yadavBest 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..
 one year ago

BoushraBest ResponseYou've already chosen the best response.1
yes understood :) then
 one year ago

meera_yadavBest 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
 one year ago

meera_yadavBest ResponseYou've already chosen the best response.0
similar equation we can write it for vertical momentum also !
 one year ago

BoushraBest ResponseYou've already chosen the best response.1
so the first one you drew above is for the horizontal momentum?
 one year ago

meera_yadavBest ResponseYou've already chosen the best response.0
dw:1341316752653:dw
 one year ago

meera_yadavBest ResponseYou've already chosen the best response.0
yep ! it's for horizontal... 2nd draw is for vertical momentum..
 one year ago

Vaidehi09Best ResponseYou've already chosen the best response.2
@meera_yadav ur first drawing....shouldn't we have vcos(theta) there...instead of sine?
 one year ago

BoushraBest 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
 one year ago

Vaidehi09Best ResponseYou've already chosen the best response.2
the eq for horizontal should be u1 = 3cos45 + vcosA
 one year ago

BoushraBest ResponseYou've already chosen the best response.1
yes, that's what I got @Vaidehi09
 one year ago

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

BoushraBest ResponseYou've already chosen the best response.1
great!!! now we can move on to 2nd equation:
 one year ago

BoushraBest ResponseYou've already chosen the best response.1
.5 mu (squared) = .5 m 3(squared) + .5 m v(squared) < why did we use this?
 one year ago

Vaidehi09Best ResponseYou've already chosen the best response.2
wait a sec, but we haven't yet found the value of u1.
 one year ago

Vaidehi09Best ResponseYou've already chosen the best response.2
thats the eq for conservation of KE
 one year ago

BoushraBest ResponseYou've already chosen the best response.1
yeah, I know,... should we label it as eq 2?
 one year ago

Vaidehi09Best ResponseYou've already chosen the best response.2
for KE, i got the eq as (u1)^2 = 3^2 + v^2
 one year ago

BoushraBest ResponseYou've already chosen the best response.1
I think the v in it should be v subscript x, correct?
 one year ago

Vaidehi09Best 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.
 one year ago

meera_yadavBest ResponseYou've already chosen the best response.0
no there's no need for the subscript vaidelhi , because K.E is a scalar quantity...
 one year ago

BoushraBest ResponseYou've already chosen the best response.1
ok, great, I'm following.. so what do we need next.
 one year ago

meera_yadavBest ResponseYou've already chosen the best response.0
I think everythings known to u know !!
 one year ago

Vaidehi09Best ResponseYou've already chosen the best response.2
we have another eq, using vertical components for momentum. and that is, vsin theta = 3sin45
 one year ago

BoushraBest ResponseYou've already chosen the best response.1
shouldn't it be 3 sin 45 =  v sin theta?
 one year ago

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

Vaidehi09Best 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
 one year ago

Vaidehi09Best ResponseYou've already chosen the best response.2
ah yes....that should be sine
 one year ago

BoushraBest 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?
 one year ago

Vaidehi09Best ResponseYou've already chosen the best response.2
yup...try it out. m also doing the same.
 one year ago

BoushraBest ResponseYou've already chosen the best response.1
ok, I'll put my answers down.. let's do that :)
 one year ago

BoushraBest ResponseYou've already chosen the best response.1
do we substitue eq 3 into 1?
 one year ago

BoushraBest ResponseYou've already chosen the best response.1
we need to solve for u1 first, right?
 one year ago

Vaidehi09Best 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
 one year ago

Vaidehi09Best ResponseYou've already chosen the best response.2
our unknowns are u, v, A. start anywhere.
 one year ago

BoushraBest ResponseYou've already chosen the best response.1
we should substitute eq 2 into 1?
 one year ago

Vaidehi09Best ResponseYou've already chosen the best response.2
yea, u can do that or vice versa. whichever is convenient to u.
 one year ago

BoushraBest ResponseYou've already chosen the best response.1
and the take the square root of it first?
 one year ago

Vaidehi09Best ResponseYou've already chosen the best response.2
that way u can get rid of u.
 one year ago

BoushraBest ResponseYou've already chosen the best response.1
do we go like this: 3 + v = 3 cos 45 + v cos A ??
 one year ago

Vaidehi09Best ResponseYou've already chosen the best response.2
how did u get 3 + v ?
 one year ago

BoushraBest ResponseYou've already chosen the best response.1
I took the square root of that
 one year ago

Vaidehi09Best ResponseYou've already chosen the best response.2
u need sqrt( 9+v^2 )
 one year ago

Vaidehi09Best ResponseYou've already chosen the best response.2
no wait....sqrt( a^2 + b^2) is NOT = a + b
 one year ago

BoushraBest 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?
 one year ago

Vaidehi09Best ResponseYou've already chosen the best response.2
before that, let me confirm something. is the angle theta = 45 ?
 one year ago

BoushraBest 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
 one year ago

Vaidehi09Best ResponseYou've already chosen the best response.2
no i mean, do u have the answers?
 one year ago

Vaidehi09Best ResponseYou've already chosen the best response.2
great...so i'm on the right path. ok proceed this way...
 one year ago

BoushraBest ResponseYou've already chosen the best response.1
I just need to know the steps, I've having a hard time substituting..
 one year ago

BoushraBest ResponseYou've already chosen the best response.1
can we start by knowing how to substitute and figure out theta?
 one year ago

Vaidehi09Best ResponseYou've already chosen the best response.2
first, swap ur RHS and LHS of eq 3 and add it to eq 1.
 one year ago

Vaidehi09Best ResponseYou've already chosen the best response.2
right hand side and left hand side of an eq.
 one year ago

BoushraBest ResponseYou've already chosen the best response.1
ok, I'd swap them and add them to the 1st equation
 one year ago

Vaidehi09Best ResponseYou've already chosen the best response.2
so ur eq 3 becomes: 3sin45 = vsinA
 one year ago

Vaidehi09Best ResponseYou've already chosen the best response.2
right. sow rite down what u got here.
 one year ago

Vaidehi09Best ResponseYou've already chosen the best response.2
so u should have now, u + 3sin45 = 3cos45 + vcosA + vsinA
 one year ago

Vaidehi09Best ResponseYou've already chosen the best response.2
cancel out 3sin45 and 3cos45. so now u have, u = v( cosA + sinA)
 one year ago

BoushraBest ResponseYou've already chosen the best response.1
is there a trig rule for cancelling them out that i should know of?
 one year ago

BoushraBest ResponseYou've already chosen the best response.1
0.707106 which is the same is cos 45
 one year ago

BoushraBest ResponseYou've already chosen the best response.1
so that's how we cancel them out.. ok!
 one year ago

Vaidehi09Best 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.
 one year ago

Vaidehi09Best ResponseYou've already chosen the best response.2
ok, moving on...substitute that eq in eq2.
 one year ago

BoushraBest ResponseYou've already chosen the best response.1
perfect, now we're left with u = v ( cos A + sin A)
 one year ago

Vaidehi09Best ResponseYou've already chosen the best response.2
u should get : v^2(sinA+cosA)^2 = 9+ v^2
 one year ago

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

Vaidehi09Best ResponseYou've already chosen the best response.2
that's right, now expand LHS and show me what u get.
 one year ago

BoushraBest ResponseYou've already chosen the best response.1
i think there' a rule saying cos A + sin A = 1?
 one year ago

Vaidehi09Best ResponseYou've already chosen the best response.2
no...that's when cosA and sinA both are squared terms
 one year ago

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

Vaidehi09Best ResponseYou've already chosen the best response.2
do u know the expansion of (a+b)^2 ?
 one year ago

BoushraBest ResponseYou've already chosen the best response.1
yes... oh wait, I made a mistake.. just a sec
 one year ago

BoushraBest ResponseYou've already chosen the best response.1
v^2 sin^2a + 2sinAcosA + cos^2 a = 9 + v^2
 one year ago

Vaidehi09Best 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.
 one year ago

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

Vaidehi09Best 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
 one year ago

Vaidehi09Best ResponseYou've already chosen the best response.2
sin2a = 2sinacosa...thats the sub i made.
 one year ago

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

Vaidehi09Best ResponseYou've already chosen the best response.2
look at the second last post. i showed how I substituted.
 one year ago

Vaidehi09Best ResponseYou've already chosen the best response.2
there's a formula : sin2A = 2sinAcosA. i used it.
 one year ago

BoushraBest ResponseYou've already chosen the best response.1
aha... ok, got it.. and now what's next?
 one year ago

BoushraBest ResponseYou've already chosen the best response.1
so the final formula here is v^2 sin2 a = 9
 one year ago

Vaidehi09Best 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)
 one year ago

Vaidehi09Best ResponseYou've already chosen the best response.2
in the eq, the RHS is 9/3sin45
 one year ago

BoushraBest ResponseYou've already chosen the best response.1
ok, the RHS is 9/3 sin 45 = 4.2426 ???
 one year ago

Vaidehi09Best ResponseYou've already chosen the best response.2
don't go on to the final values just yet. it'll only complicate things further.
 one year ago

Vaidehi09Best ResponseYou've already chosen the best response.2
continuing the above eq, we'll gte vcosA = 3 sqrt(2)
 one year ago

Vaidehi09Best ResponseYou've already chosen the best response.2
gr8! so now divide this eq with ur eq3
 one year ago

Vaidehi09Best ResponseYou've already chosen the best response.2
u should get vcosA/vsinA = 3 rt(2)/ [3/rt(2)]
 one year ago

Vaidehi09Best ResponseYou've already chosen the best response.2
which would lead us to cotA = 2 or tanA = 1/2
 one year ago

Vaidehi09Best ResponseYou've already chosen the best response.2
so now u can find A = tan^(1) [1/2]
 one year ago

BoushraBest ResponseYou've already chosen the best response.1
wait cos a/sina = tan a?
 one year ago

Vaidehi09Best ResponseYou've already chosen the best response.2
no, cosa /sina = cota = 1/tana
 one year ago

BoushraBest ResponseYou've already chosen the best response.1
yeah, i mean what's cot?
 one year ago

Vaidehi09Best ResponseYou've already chosen the best response.2
u dont know ur trigo ratios?
 one year ago

BoushraBest 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
 one year ago

Vaidehi09Best 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.
 one year ago

BoushraBest ResponseYou've already chosen the best response.1
so what do i need to look up in regards to trig in mechanics?
 one year ago

Vaidehi09Best 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.
 one year ago

Vaidehi09Best 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.
 one year ago

BoushraBest 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 :)
 one year ago

BoushraBest ResponseYou've already chosen the best response.1
yeah i know inverse ratios :)
 one year ago

Vaidehi09Best 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!
 one year ago

Vaidehi09Best 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
 one year ago

Vaidehi09Best 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
 one year ago
See more questions >>>
Your question is ready. Sign up for free to start getting answers.
spraguer
(Moderator)
5
→ View Detailed Profile
is replying to Can someone tell me what button the professor is hitting...
23
 Teamwork 19 Teammate
 Problem Solving 19 Hero
 Engagement 19 Mad Hatter
 You have blocked this person.
 ✔ You're a fan Checking fan status...
Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.