Question:
A 0.200kg ball moves with a velocity of 0.3m/s. It collides with a second ball that is at rest and has a mass of 0.1kg. After the collision, the velocity of 0.1kg ball is 0.26m/s. What is the new velocity of the first ball.
Please indicate which equation you use, what variable corresponds to each number, and how you got the number that goes with the variable.
Thanks!
To solve this problem, we can use the principle of conservation of momentum. Conservation of momentum states that the total momentum of a system remains constant if no external forces act on it.
The equation we can use is:
(m1 * v1) + (m2 * v2) = (m1 * u1) + (m2 * u2)
Where:
m1 = mass of the first ball = 0.200kg
v1 = velocity of the first ball before the collision = 0.3m/s
m2 = mass of the second ball = 0.1kg
v2 = velocity of the second ball before the collision (which is at rest) = 0m/s
u1 = velocity of the first ball after the collision (which we need to find) = ?
u2 = velocity of the second ball after the collision = 0.26m/s
Substituting the given values into the equation, we have:
(0.200kg * 0.3m/s) + (0.1kg * 0m/s) = (0.200kg * u1) + (0.1kg * 0.26m/s)
0.060kg m/s = 0.200kg u1 + 0.026kg m/s
Now, let's solve for u1:
0.060kg m/s - 0.026kg m/s = 0.200kg u1
0.034kg m/s = 0.200kg u1
Dividing both sides by 0.200kg:
0.034kg m/s / 0.200kg = u1
u1 = 0.17m/s
Therefore, the new velocity of the first ball after the collision is 0.17m/s.