1. ## collision

two smooth spheres of masses 2kg and 4kg collide obliquely . the 2 kg mass is brought to rest. the coefficient of restitution is $1/2$
prove before the impact the spheres were moving in perpendicular directions to each other.

using conservation of momentum. $4x+2y=4p+2(0)$ where x and y are velocities before impact. p is velocity after impact of 4kg

newtons experimental law $p-0/x-y =-1/2$

once i get there velocities in terms of the variables i dont know what to do

3. ## Re: collision

whats the point in latex. i could of wrote it normally and people would still understand it. doesnt seem worth it

4. ## Re: collision

your equation for Newton's experimental law cannot be correct as $p,~x,~y$ are all vectors.

There seems to be some confusion in the definition of COR but I'm going to assume it means the ratio of the relative speeds, not velocities

using your notation I get two equations

$4x + 2y = 4p$

$\dfrac{|p|}{|x-y|} = \dfrac 1 2$

$\dfrac{p\cdot p}{(x-y)\cdot(x-y)} = \dfrac 1 4$

from the first

$p = \dfrac{2x+y}{2}$

and putting this into the second we obtain

$\dfrac 1 4 \dfrac{4|x|^2 + |y|^2 + 4x\cdot y}{|x|^2 + |y|^2 - 2 x \cdot y} = \dfrac 1 4$

$\dfrac{4|x|^2 + |y|^2 + 4x\cdot y}{|x|^2 + |y|^2 - 2 x \cdot y} = 1$

$4|x|^2 + |y|^2 + 4x\cdot y = |x|^2 + |y|^2 - 2 x \cdot y$

$3|x|^2 = - 6 x \cdot y$

$x \cdot y = -\dfrac 1 2 |x|^2 \neq 0$

So either I'm misinterpreting COR, or there is a problem with the question or both.

5. ## Re: collision

I'm seeing another definition of COR for oblique collisions.

In this case they are defining

$COR = \dfrac{\text{speed of separation}}{\text{speed of approach}}$

Is this what you are supposed to use?

6. ## Re: collision

the COR equation i use is v1-v2/u1-u2 =-e

im trying to split there velocities into i and j components

7. ## Re: collision

Originally Posted by markosheehan
the COR equation i use is v1-v2/u1-u2 =-e

im trying to split there velocities into i and j components
what you've got there is the ratio of two vectors.

8. ## Re: collision

Ok. So i can prove they move perpendicular to each other before the collision. It's in the question. The j components don't change as it's along the i axis. This means they have to be moving perpendicular to each other.

I'm still having trouble working out there velocities before and after. I'm not using the equation. 2x+4(0)=4a. And a-0/0-x. =-.5. Sadly these equations are the same.