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Two identical objects (such as billiard balls) have a
Chapter 8, Problem 28(choose chapter or problem)
Problem 28PE
Two identical objects (such as billiard balls) have a onedimensional collision in which one is initially motionless. After the collision, the moving object is stationary and the other moves with the same speed as the other originally had. Show that both momentum and kinetic energy are conserved.
Questions & Answers
QUESTION:
Problem 28PE
Two identical objects (such as billiard balls) have a onedimensional collision in which one is initially motionless. After the collision, the moving object is stationary and the other moves with the same speed as the other originally had. Show that both momentum and kinetic energy are conserved.
ANSWER:
Solution 28 PE
Step 1 of 3
The conservation of momentum and kinetic energy of the system can be proved by showing that the total momentum and kinetic energy of the system before collision and after collision are equal.
Let us name the two billiard balls as 1 and 2 of which ball 1 is colliding with a stationary ball 2 . The initial velocities of the billiard balls 1 and 2 be and
respectively, m1 and m2 be their masses .The masses are equal as they are identical billiard balls. So, m1= m2 = m. Now, let
and
be the final velocities of the ball 1 and 2 respectively.
After, they have a one dimensional collision, the ball 2 starts moving with a same velocity has the ball 1 had originally whereas, the ball 1 becomes stationary.