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Momentum and Elastic Collisions

by ndoc
Tags: collisions, elastic, momentum
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ndoc
#1
Nov5-09, 06:57 PM
P: 13
1. The problem statement, all variables and given/known data
In a pool game, the cue ball, which has an initial speed of 8.0 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 30 to the original direction of the cue ball.


2. Relevant equations
V8 = Velocity of 8-ball
Vc = Velocity of cue ball

(1)Epx = m*V8*cos(30) + m*Vc*cos(x) = m*8
(2)Epy = m*V8*sin(30) + m*Vc*sin(x) = 0
(3).5*m*Vi^2 = .5*m*V8^2 + .5*m*Vc^2


3. The attempt at a solution
While these equations are technically solvable, they are nearly impossible by hand. Solving (3) for one velocity and using substitution twice I get:
sin(x)^2 -cos(30)*cos(x) + sin(30)*cos(30)*cos(x) - sin(30)*cos(x)^2 = -1/8

Is there an easier way to solve this since I know I will not be able to solve this equation myself?
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rl.bhat
#2
Nov5-09, 07:48 PM
HW Helper
P: 4,435
(1)Epx = m*V8*cos(30) + m*Vc*cos(x) = m*8
(2)Epy = m*V8*sin(30) + m*Vc*sin(x) = 0

Rewrite these two equations as
m*V8*cos(30) = m*8 - m*Vc*cos(x) -------(1)
m*V8*sin(30) = - m*Vc*sin(x) ----------(2)
Square both sides of eq.1 and 2 and add them. After simplification you will get the value of vc*cos(x)
From the conservation of energy equation, find the value of vc. Then you can find the angle x.
ndoc
#3
Nov5-09, 07:56 PM
P: 13
Awesome, thanks so much!


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