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Mechanics 2 Collision

I have a question in Chapter 4 M2 Collisions, which my teacher also failed to answer,
it is:
A sphere of mass m1 moving with speed u1 collides directly with a similar sphere of mass m2 moving with speed u2 in the same direction (u1>u2). The coefficient of restitution between the two spheres is e. Show that the loss of kinetic energy E due to the collisionn satisfies the equation:

2(m1 + m2) E = m1m2(u1 - u2)^2 (1- e^2)

Thanks, and I appreciate it!! :biggrin:

Reply 1

logic123

just work out speeds in terms of U and E after the collision then sub into Kinectic energy befor eand after, subtract and you have your asnwer.

Reply 2

Medicine Man

16

Oh i did this question today at school!!!!
my teacher had to photocopy his soolution for all of us - noone could understand it.

Reply 3

Oh I Really Don't Care

17

...

...

\frac{3}{2}

A4 sheets for this question. .........

Reply 4

Medicine Man

16

Here's my teachers solution.

And even he said it was definitely in his top 10 Maths/Further Maths questions he'd ever done.

Pretty nasty tbh.

m2 collisions.jpg194.0KB

Reply 5

azhao

3

Dude that question was so horrible, did it last year and it took like 3 sides of A4!!!

Reply 6

hellboyy

OP

thx ppl

Reply 7

bt_1000

2

I asked the same question 4 weeks ago, and was told not to bother
http://www.thestudentroom.co.uk/showthread.php?p=16464595#post16464595

Reply 8

hellboyy

OP

well now u have the answer!!

Reply 9

Medicine Man

16

thanks to me - well my very smart maths teacher - but I'll take the credit!! :tongue:

Reply 10

ghostwalker

17

Sorry, couldn't resist!
I wouldn't normally do full workings, but in this case....

Here is the initial set up, and the rest of the working is in the spoiler:

Conservation of momentum gives:

m_1u_1+m_2u_2=m_1v_1+m_2v_2

Rearranging we get:

m_1(u_1-v_1)=m_2(v_2-u_2)

Thus:

\displaystyle \frac{m_1}{m_2}=\frac{v_2-u_2}{v_1-u_1}

And call this equation (1)

Consideration of restitution gives:

v_2-v_1=-e(u_2-u_1)

And call this equation (2)

Now loss in KE is E. So:

E=\frac{1}{2}m_1(u_1^2-v_1^2)+\frac{1}{2}m_2(u_2^2-v_2^2)

Spoiler

(edited 13 years ago)

Reply 11

ShafeeqSRS

Medicine Man

Here's my teachers solution.

And even he said it was definitely in his top 10 Maths/Further Maths questions he'd ever done.

Pretty nasty tbh.

Dear Medicine man, if your teacher has solved question 8, what about question 7. Please tell me that you have a similar working out for question 7. I am stuck on it for the past 3 days. I urgently need help now.

Thanks
:eek3:

Reply 12

Medicine Man

16

ShafeeqSRS

Dear Medicine man, if your teacher has solved question 8, what about question 7. Please tell me that you have a similar working out for question 7. I am stuck on it for the past 3 days. I urgently need help now.

Thanks
:eek3:

sent you a PM

but you can always ask on the Maths forum, someone should be able to help you. :smile:

Reply 13

ShafeeqSRS

Medicine Man

sent you a PM

but you can always ask on the Maths forum, someone should be able to help you. :smile:

What is a PM?
How do I enter the maths forum?

(I am a new member)

Thanx

Reply 14

Medicine Man

16

ShafeeqSRS

What is a PM?
How do I enter the maths forum?

(I am a new member)

Thanx

PM is a private message =]

To post a question in the maths forum, just click the link below and select "new thread" near the top of the page.

http://www.thestudentroom.co.uk/forumdisplay.php?f=38

Reply 15

Tiag0

If you use the fact that the kinetic energy loss does not change if you change your referential (you can think of it as the dissipation of energy only depends on the relative velocity, or you can just prove it), you can simplify the problem by making (before the colision) the first ball move at V and the second one not moving. The algebra gets way more simple.

Reply 16

username1162972

18

Original post by Tiag0

If you use the fact that the kinetic energy loss does not change if you change your referential (you can think of it as the dissipation of energy only depends on the relative velocity, or you can just prove it), you can simplify the problem by making (before the colision) the first ball move at V and the second one not moving. The algebra gets way more simple.