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
1.44 m/s
1.44 m/s
36 m/s
36 m/s
4 m/s
To solve this problem, we can apply the principle of conservation of momentum. The total momentum before the collision is equal to the total momentum after the collision in a closed system.
Before the collision:
Momentum of first ball = mass × velocity
Momentum of second ball = mass × velocity
After the collision:
Momentum of first ball = 0 (since it stops)
Momentum of second ball = mass × velocity2
Now, let's calculate the velocity2 of the second ball using the conservation of momentum equation:
(mass of first ball × velocity of first ball) + (mass of second ball × velocity of second ball) = (mass of first ball × 0) + (mass of second ball × velocity2)
(0.6 kg × 12 m/s) + (0.6 kg × 12 m/s) = (0.6 kg × 0) + (0.6 kg × velocity2)
14.4 kg·m/s + 14.4 kg·m/s = 0 + (0.6 kg × velocity2)
28.8 kg·m/s = 0.6 kg × velocity2
Dividing both sides by 0.6 kg:
velocity2 = 28.8 kg·m/s / 0.6 kg
velocity2 = 48 m/s
Now, let's calculate the velocity of the third ball using the same principle of conservation of momentum:
(mass of second ball × velocity2) + (mass of third ball × velocity3) = (mass of second ball × final velocity of second ball) + (mass of third ball × velocity3)
(0.6 kg × 48 m/s) + (0.2 kg × velocity3) = (0.6 kg × final velocity of second ball) + (0.2 kg × velocity3)
28.8 kg·m/s + 0.2 kg × velocity3 = 0.6 kg × final velocity of second ball + 0.2 kg × velocity3
Rearranging the equation, we get:
0.2 kg × velocity3 - 0.2 kg × velocity3 = 0.6 kg × final velocity of second ball - 28.8 kg·m/s
0 = 0.6 kg × final velocity of second ball - 28.8 kg·m/s
Solving for final velocity of the second ball:
0.6 kg × final velocity of second ball = 28.8 kg·m/s
final velocity of second ball = 28.8 kg·m/s / 0.6 kg
final velocity of second ball = 48 m/s
As we can see, the final velocity of the second ball matches the velocity2 value we calculated earlier. This means that the collision between the second and third ball is elastic (no energy loss). Therefore, the velocity of the third ball is also 48 m/s.
The correct answer is: 48 m/s.