Two billiard balls each of mass 0.05 \(\text {kg}\) moving in opposite directions with speed 6 \(\text m \,\text s^{-1}\)collide and rebound with the same speed. What is the impulse imparted to each ball due to the other ?
Solution and Explanation
Mass of each ball = 0.05 \(\text {kg}\)
Initial velocity of each ball = 6 \(\text m/\text s\)
Magnitude of the initial momentum of each ball, \(p_i\) \(=\) 0.3 \(\text {kg}\) \(\text m/\text s\)
After collision, the balls change their directions of motion without changing the magnitudes of their velocity.
Final momentum of each ball, \(p_f\) \(=\) –0.3 \(\text {kg}\) \(\text m/\text s\)
Impulse imparted to each ball = Change in the momentum of the system
\(=\) \(p_f-p_i\)
= – 0.3 – 0.3 = –0.6 \(\text {kg}\) \(\text m/\text s\)
The negative sign indicates that the impulses imparted to the balls are opposite in direction.
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Concepts Used:
Newtons Laws of Motion
Newton’s First Law of Motion:
Newton’s 1st law states that a body at rest or uniform motion will continue to be at rest or uniform motion until and unless a net external force acts on it.
Newton’s Second Law of Motion:
Newton’s 2nd law states that the acceleration of an object as produced by a net force is directly proportional to the magnitude of the net force, in the same direction as the net force, and inversely proportional to the object’s mass.
Mathematically, we express the second law of motion as follows:
Newton’s Third Law of Motion:
Newton’s 3rd law states that there is an equal and opposite reaction for every action.