A small ball with a mass of 0.6 kg and a velocity of 12 m/s hits another ball with the same mass. The first ball stops moving, and the second ball then moves forward and hits a third ball with a mass of 0.2 kg. If the system is closed, what is the velocity of the third ball? (1 point) Responses 30 m/s 30 m/s 36 m/s 36 m/s 1.44 m/s 1.44 m/s 4 m/s
To solve this problem, we can use the principle of conservation of momentum. According to this principle, the total momentum before the collision is equal to the total momentum after the collision in a closed system.
Let's first calculate the initial momentum before the collision:
Initial momentum = mass * velocity
Momentum of the first ball = 0.6 kg * 12 m/s = 7.2 kg m/s
Since the second ball has the same mass and starts at rest, its initial momentum is 0 kg m/s.
Therefore, the total initial momentum before the collision is 7.2 kg m/s.
After the collision, the first ball stops moving, and the second ball moves forward with an unknown velocity. Let's call this velocity V.
The total mass of the system after the collision is 0.6 kg + 0.6 kg = 1.2 kg.
Using the conservation of momentum principle, the total momentum after the collision is equal to the total initial momentum:
Total momentum after collision = 7.2 kg m/s
Total momentum after the collision = (0.6 kg * 0 m/s) + (0.6 kg * V)
So, 7.2 kg m/s = 0 kg m/s + 0.6 kg * V
Simplifying the equation, we have:
7.2 kg m/s = 0.6 kg * V
Dividing both sides by 0.6 kg:
12 kg m/s = V
Therefore, the velocity of the second ball is 12 m/s.
Now, using the same principle of conservation of momentum, we can calculate the velocity of the third ball.
The total mass of the system after the second collision is 0.6 kg + 0.2 kg = 0.8 kg.
Let's call the velocity of the third ball W.
Using the conservation of momentum principle, the total momentum after the second collision is equal to the total initial momentum:
Total momentum after second collision = 0.6 kg * 0 m/s + 0.2 kg * W
Total momentum after second collision = 7.2 kg m/s
So, 0.2 kg * W = 7.2 kg m/s - 0 kg m/s
0.2 kg * W = 7.2 kg m/s
Dividing both sides by 0.2 kg:
W = 7.2 kg m/s / 0.2 kg
W = 36 m/s
Therefore, the velocity of the third ball is 36 m/s.
So, the correct answer is 36 m/s.