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Class 29: More collisions Simple collision problem in 1D Before - - PowerPoint PPT Presentation
Class 29: More collisions Simple collision problem in 1D Before - - PowerPoint PPT Presentation
Class 29: More collisions Simple collision problem in 1D Before collision: m 1 m 2 #2 v 2i v 1i #1 After collision: m 2 m 1 #1 v 1f v 2f #2 Equation of motion: m 1 v 1i + m 2 v 2i = m 1 v 1f + m 2 v 2f Can solve for any one unknown from v 1i , v
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“Quality” of collision (coefficient of restitution) m1 After collision: #1 #2 #2 #1 Coefficient of restitution m2 v1i v2i m1 m2 v2f v1f
collision before velocity relative collision after velocity relative v v v v v v v v e
2i 1i 2f 1f 1i 2i 1f 2f
Warning: not in textbook, we are using a different approach here.
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Simple collision problem in 1D Before collision: m1 After collision: #1 #2 #2 #1
Equation of motion: With e given, can solve for any two unknowns from v1i, v2i, v1f and v2f .
m2 v1i v2i m1 m2 v2f v1f
v v v v e v m v m v m v m
1i 2i 1f 2f 2f 2 1f 1 2i 2 1i 1
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Example 2 Before collision: 2kg 4kg 4m/s 5m/s After collision: 2kg 4kg #1 #2 #2 #1
What are V1f and V2f if e = 1/3 ?
v1f=? v2f=?
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Meaning of e
- 1. 0 e 1
- 2. e is related to the mechanical energy lost in the
collision.
Warning: not in textbook, we are using a different approach here.
e 1
Inelastic collisions e=1: No mechanical energy is lost. Elastic collision. e=0: Maximum mechanical energy is lost. Completely inelastic collision. Objects stick together after collision.
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Example 3 Before collision: 2kg 4kg 4m/s 5m/s After collision: 2kg 4kg #1 #2 #2 #1
What are V1f and V2f if this is an elastic collision?
v1f=? v2f=?
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Example 5 Before collision: 2kg 4kg 4m/s 5m/s After collision: 2kg 4kg #1 #2 #2 #1
What is Vf if the balls stick together and move with the same velocity after the collision? How much energy is lost during collision?
vf=?
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