1. ## collision

a smooth sphere of A of mass km moving with speed u collides directly with a smooth sphere B of mass m moving in the same direction with speed ku. A is brought to rest by the collision. find the speed of B after the collision in terms of k and u and prove k is greater or equal to 1/3

i can do the first part but not the second. using the conservation of momentum formula km(u)+m(ku)=m(v1)+km(0) so uk+ku=v1 2ku=v1
using the coefficient of restitution formula 0-u/2ku-ku=-e this doesnt seem to help

2. ## Re: collision

Originally Posted by markosheehan
a smooth sphere of A of mass km moving with speed u collides directly with a smooth sphere B of mass m moving in the same direction with speed ku. A is brought to rest by the collision. find the speed of B after the collision in terms of k and u and prove k is greater or equal to 1/3

i can do the first part but not the second. using the conservation of momentum formula km(u)+m(ku)=m(v1)+km(0) so uk+ku=v1 2ku=v1
using the coefficient of restitution formula 0-u/2ku-ku=-e this doesnt seem to help
$km \cdot u + m \cdot ku = m v_{fB} \implies v_{fB} = 2ku$

$KE_f = \dfrac{1}{2}m(2ku)^2 = 2mk^2u^2$

$KE_0 = \dfrac{1}{2}kmu^2 + \dfrac{1}{2}m(ku)^2 = \dfrac{1}{2}kmu^2(1+k)$

$KE_0 \ge KE_f$

$\dfrac{1}{2}kmu^2(1+k) \ge 2mk^2u^2$

solve the inequality for $k$ ...

3. ## Re: collision

they don't give you a COR so all you can do is assume that the kinetic energy in the system before the collision is greater than or equal to that after the collision.

that relationship and the conservation of momentum give you the two equations you need to solve this.

I'm showing that $k \leq \dfrac 1 3$ though

4. ## Re: collision

i get it now. i had not thought of looking at their kinetic energies.