Question

Two billards balls each of mass o.o5 kg moving in opposite direction with each speed of 6 m/s collide and rebound with same speed what is the impulse imparted to each other due to the other ball .​

Answer 1

Solution :-

Given :-

Mass of each ball = 0.05 kg

Speed of each ball = 6m/s

Initial momentum of each balls :-

$\longrightarrow \sf P_i = mv \\\\\longrightarrow P_i = 0.05 \times 6 \\\\\longrightarrow\bf P_i = 0.3 \ kg \ m/s$

After collision, the two balls change their directions of motion without changing the magnitudes of their velocity.

Final momentum of each balls :-

$\longrightarrow \sf P_f = 0.05 \times -6 \\\\\longrightarrow \bf P_f = -0.3 \ kg \ m/s$

Impulse imparted to each ball = Change in momentum

$\longrightarrow \sf I = P_f-P_i \\\\\longrightarrow I = -0.3-0.3 \\\\\longrightarrow \bf I = -0.6$

The negative sign indicates that the impulses imparted to the balls are in opposite direction.

Answer 2

Explanation:

Solution :-

Given:-

The momentum of the ball can be calculated as

p = m× v

Where, ‘m’ is the mass of the ball

and ‘v’ is the velocity of the ball

Mass of each ball = 0.05 kg

Initial velocity of each ball =6m/s

Magnitude of the momentum of each balls :-

$\longrightarrow \sf P_i = mv \\\\\longrightarrow P_i = 0.05 \times 6 \\\\\longrightarrow\bf P_i = 0.3 \ kg \ m/s$

The balls rebound after the collision thus, they change directions but the magnitude of the velocity remains the same

Final momentum of first ball :-

$\longrightarrow \sf P_f = 0.05 \times -6 \\\\\longrightarrow \bf P_f = -0.3 \ kg \ m/s$

Final momentum of second ball

$\longrightarrow \sf P_f = 0.05 \times -6 \\\\\longrightarrow \bf P_f = 0.3 \ kg \ m/s$

Impulse imparted to first ball:

$\longrightarrow \sf I = P_f-P_i \\\\\longrightarrow I = -0.3-0.3 \\\\\longrightarrow \bf I = -0.6 \ kg \ m/s$

The negative sign is because the impulse imparted to each of the balls are in opposite directions. the impulse imparted to each ball due to the other is 0.6 N in opposite directions.