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posted by  Daffy on 7/17/2008 4:26:55 PM  |  status: Closed  

Oblique Central Impact

Course Textbook Chapter Problem
Classical Mechanics Engineering Mechanics Statics and Dynamics Fifth Edition 16 16.80
Question Details:
Ball A travels in the direction shown with a velocity of 2 m/s and strikes ball B which starts at rest then travels at a 45 degree angle as shown.  The balls are of equal mass and the coefficient of restitution is e = 1.
What are the velocity vectors of the two balls just after the impact?
     
    
 
 
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posted by zsm28 on 7/17/2008 8:45:37 PM  |  status: Live
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Response Details:
what is the speed of B before impact?
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posted by Daffy on 7/17/2008 11:09:25 PM  |  status: Live
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Response Details:
B is stationary before impact.
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posted by zsm28 on 7/18/2008 2:53:31 AM  |  status: Live
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Response Details:
v = 2 m/s, mA = mB = m
velocities after impact: vA and vB
momentum conservation:
mv = mvA + mvB (vector sum)
∴v = vA + vB
It means these 3 vectors form a triangle.
e = 1 means the impact is elastic,
mv2/2 = mvA2/2 + mvB2/2
∴v2 = vA2 + vB2
It means these 3 vectors form a right triangle.
notice the angle between v and vB is 45o,
so the magnitude vA = vB = vsin(45) = 2/√2 = 1.41 m/s
If v is to the north, vB is to the northwest, then vA is to the northeast.
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