M2 Collsions

To find e, you have to form Moment*velocity & Coefficient of Resititution equations for the collision between A&B and B&C, then solve the equations.

If that doesn't help, ask :smile:

Reply 4

OP

Gemini

I'll answer :smile:

I'm afraid your working for part a is wrong, you have to prove that the speed of A afterwards is 0, so you can't assume it.

i proved that e=1/2 but ive got a answer -ve. thats the only thing that bothered me.

Reply 5

OP

cheers, i'll have a go at that...is this for part a?

Reply 6

Yup.

I think your problem is that the speed of A changes from 8 to 0. This makes e=0.5

Reply 7

OP

Gemini

Yup.

I think your problem is that the speed of A changes from 8 to 0. This makes e=0.5

for A&B i have got the following equations:
0.8 = -0.1(x) + 0.2(y)
&
8e = y-x

im confused from here on

Reply 8

Right, both those equations are fine.
Try looking at the collision between B&C - you'll have to introduce a new variable z.

Reply 9

OP

Gemini

Right, both those equations are fine.
Try looking at the collision between B&C - you'll have to introduce a new variable z.

okay...im really :confused:

now as i don't knw the speed of B, do i rename it to Z, if so what do i do with the other equations

Reply 10

I'll write out what I did,
Right, once A has collided with B, B moves away with a speed of y. C is at rest, and you know that C has a speed of 2 after the collision. So, the only thing you don't know is the speed of B after its collision with C, lets call it z.

So: 0.2y+0.4*0 = 0.2z + 0.4*2
=> y = z + 4
Also: e= (2-z)/ (y-0)
=> z= 2-ey

You can then subsitute z into the first equation I found:
y=2-ey+4
=> (1+e)y=6
=> y=6/(1+e)

From the equations you worked out above:
1) x+2y=8 & 2) x=y-8e
=> 3y=8+8e
=> y=(8/3)(1+e)

So from here you have two equations you can put together to get:
(8/3) (1+e) = 6/ (1+e)
=> (1+e)^2 =9/4
=> e+1=3/2 (e>0 , so it can't =-3/2)
=> e=1/2

Not a nice question :smile:

Reply 11

OP

Gemini

I'll write out what I did,
Right, once A has collided with B, B moves away with a speed of y. C is at rest, and you know that C has a speed of 2 after the collision. So, the only thing you don't know is the speed of B after its collision with C, lets call it z.

So: 0.2y+0.4*0 = 0.2z + 0.4*2
=> y = z + 4
Also: e= (2-z)/ (y-0)
=> z= 2-ey

You can then subsitute z into the first equation I found:
y=2-ey+4
=> (1+e)y=6
=> y=6/(1+e)

From the equations you worked out above:
1) x+2y=8 & 2) x=y-8e
=> 3y=8+8e
=> y=(8/3)(1+e)

So from here you have two equations you can put together to get:
(8/3) (1+e) = 6/ (1+e)
=> (1+e)^2 =9/4
=> e+1=3/2 (e>0 , so it can't =-3/2)
=> e=1/2

Not a nice question :smile:

how would i show they all come to rest?

Reply 12