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 2i , v 1f and v 2f .
Warning: not in textbook, we are using a different approach here. “Quality” of collision (coefficient of restitution) m 1 m 2 #2 v 2i v 1i #1 After collision: m 2 m 1 #1 v 1f v 2f #2 Coefficient of restitution v v v v 2f 1f 1f 2f e v v v v 2i 1i 1i 2i relative velocity after collision relative velocity before collision
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 v m v m v m v 1 1i 2 2i 1 1f 2 2f v v 2f 1f e v v 2i 1i With e given, can solve for any two unknowns from v 1i , v 2i , v 1f and v 2f .
Example 2 Before collision: 4kg 2kg 4m/s 5m/s #1 #2 After collision: 4kg 2kg #1 v 2f =? v 1f =? #2 What are V 1f and V 2f if e = 1/3 ?
Warning: not in textbook, we are using a different approach here. Meaning of e 1. 0 e 1 2. e is related to the mechanical energy lost in the collision. e 0 1 Inelastic collisions e=0: e=1: Maximum mechanical energy No mechanical is lost. energy is lost. Completely inelastic collision. Elastic collision . Objects stick together after collision.
Example 3 Before collision: 4kg 2kg 4m/s 5m/s #1 #2 After collision: 4kg 2kg #1 v 1f =? v 2f =? #2 What are V 1f and V 2f if this is an elastic collision?
Example 5 Before collision: 4kg 2kg 4m/s 5m/s #1 #2 After collision: 4kg 2kg #1 #2 v f =? What is V f if the balls stick together and move with the same velocity after the collision? How much energy is lost during collision?
Example 4 Balls have equal mass Before collision: m m (at rest) #1 #2 After collision: m m #1 v 1f =? v 2f =? #2 What are V 1f and V 2f if this is an elastic collision?
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