The mass of the second ball after the collision can be found using the conservation of momentum, with calculations showing that the mass is 0.67 kg, based on the speeds given before and after the collision.
To solve for the mass of the second ball after a collision, we apply the principle of conservation of momentum, as the system is isolated and no external forces act on it (assuming no air resistance and that the cord's influence is negligible during the collision). The formula for conservation of momentum is:
m1 * v1 + m2 * v2 = (m1 + m2) * vf
Where:
m1 is the mass of the first ball (1.0 kg)v1 is the velocity of the first ball before collision (2.0 m/s)m2 is the mass of the second ball (unknown)v2 is the velocity of the second ball before collision (0 m/s since it's at rest)vf is the velocity of both balls after collision (1.2 m/s)
Substituting the known values:
(1.0 kg * 2.0 m/s) + (m2 * 0 m/s) = (1.0 kg + m2) * 1.2 m/s
This simplifies to:
2.0 kg*m/s = 1.2 m/s * (1.0 kg + m2)
Dividing both sides by 1.2 m/s gives:
1.6667 kg = 1.0 kg + m2
So, m2 = 1.6667 kg - 1.0 kg = 0.6667 kg, which rounded to two decimal places is 0.67 kg (Answer A).