coeffcient of restitution for collisions between the two balls

[dopi]

A red snooker ball of mass m and radius a is at rest on the snooker

table. The white ball's centre is travelling along a line that is tangent

to the red ball. The white ball also has a mass m and radius a. The

coeffcient of restitution for collisions between the two balls is e.

 

(a) Show that the speed of the red ball after collision is

(square-root 3)/4 * (1 + e)

times the speed of the white ball before the collision.

 

(b) Find the angle that the white ball's path is deflected by.

 

© Show that no energy is lost in the collision if e = 1.

 

Does anyone have any hints on how to solve this or know how to solve this

thankz

[swansont]

Momentum will be conserved, for starters, since there is no net external force on the system. The coefficient of restitution should give you information about the kinetic energy; while KE will not be conserved in an inelastic collision, the coefficient should quantify by how much it is not conserved.

[dopi]

Thankz, but iv been stuck on part (b) of the question for a while now, i was wondering if anyone knows how to solve it

 

A red snooker ball of mass m and radius a is at rest on the snooker

table. The white ball's centre is travelling along a line that is tangent

to the red ball. The white ball also has a mass m and radius a. The

coeffcient of restitution for collisions between the two balls is e.

 

(a) Show that the speed of the red ball after collision is

(square-root 3)/4 * (1 + e)

times the speed of the white ball before the collision.

 

(b) Find the angle that the white ball's path is deflected by.

[5614]

If you model it in 2D then you could calculate the horizontal and vertical components of the initial and final velocity. Using that you can set up simple trig equation to find the angle from the two "lengths" of a triangle, using the velocity as the length.

[dopi]

Momentum will be conserved, for starters, since there is no net external force on the system. The coefficient of restitution should give you information about the kinetic energy; while KE will not be conserved in an inelastic collision, the coefficient should quantify by how much it is not conserved.

 

iv tried that...however i cant seem to get the correct answer...i get v=u(e+1)m using the COR formula and momentum formula...cant seem to link the kenetic energy formula and get the (root3)/ 4 part...is there any one who can show me part (a) please

[5614]

Kinetic energy = [math]\frac{1}{2} m v^2 [/math] where m is mass and v is the velocity (squred)... just plug in your values.

 

The value [math]\frac{\sqrt{3}}{4}[/math] sounds like its from an angle, just because [math]\cos ( 30 ) = \frac{\sqrt{3}}{2} [/math] so if you remember that it's [math]\frac{1}{2} m v^2 [/math] with an emphasis on the [math]\frac{1}{2}[/math] you can combine the cos(30) and half to get your [math]\frac{\sqrt{3}}{4}[/math]... now obviously this is working backwards, but then I'm trying to help you in the right direction and not actually do it for you, now maybe that helps in pointing you in the right direction. Although note it could be crap, dunno, it's just what came into my mind when I read the question.

[swansont]

I think the angle can be derived from the impact parameter (The white ball's centre is travelling along a line that is tangent to the red ball.)