A 0.50 kg ball traveling at 6.0 m/s collides head-on with a 1.00 kg ball moving in the opposite direction at a velcity of -12.0 m/s. The 0.50 kg ball moves away at -14 m/s after the collision. Find the velocity of the second ball.
To find the velocity of the second ball after the collision, we can use the law of conservation of momentum. The law of conservation of momentum states that the total momentum before a collision is equal to the total momentum after the collision, provided no external forces act on the system.
The momentum, p, of an object is given by the product of its mass, m, and its velocity, v. Mathematically, it is expressed as:
p = m * v
Since the two balls are moving in opposite directions, we need to assign opposite signs to their velocities. Let's denote the velocity of the first ball as v1, the velocity of the second ball as v2, and the mass of the first ball as m1 (0.50 kg) and the mass of the second ball as m2 (1.00 kg).
Before the collision, the total momentum of both balls is:
p_total_initial = m1 * v1 + m2 * v2
After the collision, the total momentum of both balls is:
p_total_final = m1 * v1' + m2 * v2'
where v1' and v2' are the velocities of the respective balls after the collision.
Using the given information, we can set up the momentum equations:
m1 * v1 + m2 * v2 = m1 * v1' + m2 * v2' (1)
We also know the velocity of the first ball after the collision is -14 m/s:
v1' = -14 m/s
Substituting this value into equation (1), we can solve for the velocity of the second ball, v2':
0.50 kg * 6.0 m/s + 1.00 kg * (-12.0 m/s) = 0.50 kg * (-14 m/s) + 1.00 kg * v2'
3.0 kg*m/s - 12.0 kg*m/s = -7.0 kg*m/s + v2'
-9.0 kg*m/s = -7.0 kg*m/s + v2'
v2' = -9.0 kg*m/s + 7.0 kg*m/s
v2' = -2.0 kg*m/s
Therefore, the velocity of the second ball after the collision is -2.0 m/s.