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elastic collision

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Karma Points: 200
Respect (75%):
Date Posted: 7/24/2008 10:53:44 AM  Status: Live
elastic collision
Course Textbook Chapter Problem
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Question Details:
In a pool game, the cue ball, which has an initial speed of 6.0 m/s, make an elastic collision with the eight ball, which is initially at rest. After the collision, the eight ball moves at an angle of 20° to the original direction of the cue ball.
(a) Find the direction of motion of the cue ball after the collision.
              the angle =  ? degree ° (from the original line of motion)
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Expert
Karma Points: 895
(Kansas State University)
Date Posted: 7/24/2008 2:48:04 PM  Status: Live
Asker's Rating: This answer has not been rated. If you asked this question, then please login.   
Response:
The momentum is conserved in elastic collisions.
m1v1i=m1v1f+m2v2f
Consider this diagram:

Before the collision there is no momentum in the y-direction
Therefore, after the collision the sum of the momentum in the y-direction will be zero as well

Now, I'm going to assume that they have the same mass since it didn't state otherwise in the problem. Therefore, given the equation:
m1v1i=m1v1f+m2v2f
Apply it to just the y-direction
0=m1v1f+m1v2f
Therefore,:
v1f=-v2f (y-direction)

Basically, all this means that they are shooting off in exactly opposite directions after they collide
so the angle will be
-20o
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Oracle
Karma Points: 15,230
Date Posted: 7/24/2008 2:53:35 PM  Status: Live
Asker's Rating: Lifesaver   
Response:
the angle is 90 - 20 = 70o

both balls have same mass, so
momentum conservation:
vo = v1 + v2
it is a vector form, and means the 3 vectors form a triangle.
energy conservation:
vo2 = v12 + v22
it means the 3 vectors form a right triangle.
so v1 and v2 are perpendicular to each other.
since the angle between v and v1 is 20o, so the angle between v and v2 is 70o
tmark's Comment:
you are so smart!

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Karma Points: 291
Date Posted: 7/24/2008 3:09:45 PM  Status: Live
Asker's Rating: Somewhat Helpful   
Response:
Principle of Conservation of Momentum tells us that the momentum before collision and the momentum after collision will always be the same.
 
We know, Momentum = Mass * Velocity
Here, Note that Velocity is a vector quantity.
 
Momentum before collision = M1 * V
The momentum is a vector quantity acting in the direction of V.
After collision,
Momentum = M1 * V1 + M2 * V2
Here, the momentum is also a vector quantity. Vector quantity's direction here is determined by directions of V2 and V1.
The resultant of V2 and V1 has to be in the V direction.
So, V1 is perpendicular to V2 and as a result of which V2 makes an angle of 70 degrees to V.
tmark's Comment:
thank you, I already got it



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