1. 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. This principle states that the total momentum before a collision is equal to the total momentum after the collision, as long as there are no external forces acting on the system.
Let's assign variables to the given values:
m1 = mass of the first ball = 0.200 kg
v1 = velocity of the first ball before the collision = 0.3 m/s
m2 = mass of the second ball = 0.1 kg
v2 = velocity of the second ball before the collision (at rest) = 0 m/s
v2' = velocity of the second ball after the collision = 0.26 m/s
We can use the equation for momentum:
m1v1 + m2v2 = m1v1' + m2v2'
Substituting the given values:
(0.200 kg)(0.3 m/s) + (0.1 kg)(0 m/s) = (0.200 kg)(v1') + (0.1 kg)(0.26 m/s)
0.06 kg·m/s = 0.200 kg·v1' + 0.026 kg·m/s
Now, let's solve for v1':
0.06 kg·m/s - 0.026 kg·m/s = 0.200 kg·v1'
0.034 kg·m/s = 0.200 kg·v1'
v1' = 0.034 kg·m/s / 0.200 kg
v1' ≈ 0.17 m/s
Therefore, the new velocity of the first ball after the collision is approximately 0.17 m/s.
To solve this problem, we can use the principle of conservation of momentum, which states that the total momentum before a collision is equal to the total momentum after the collision.
The equation we can use is:
m1 * v1_initial + m2 * v2_initial = m1 * v1_final + m2 * v2_final
Where:
m1 = mass of the first ball (0.200 kg)
v1_initial = initial velocity of the first ball (0.3 m/s)
m2 = mass of the second ball (0.1 kg)
v2_initial = initial velocity of the second ball (0 m/s since it is at rest)
v1_final = final velocity of the first ball (unknown)
v2_final = final velocity of the second ball (0.26 m/s)
Plugging in the given values into the equation, we have:
(0.200 kg * 0.3 m/s) + (0.1 kg * 0 m/s) = (0.200 kg * v1_final) + (0.1 kg * 0.26 m/s)
Simplifying the equation, we have:
0.06 kg⋅m/s = 0.2 kg⋅v1_final + 0.026 kg⋅m/s
Next, we isolate v1_final by moving the terms to one side:
0.06 kg⋅m/s - 0.026 kg⋅m/s = 0.2 kg⋅v1_final
0.034 kg⋅m/s = 0.2 kg⋅v1_final
Finally, we divide both sides by 0.2 kg to solve for v1_final:
v1_final = 0.034 kg⋅m/s / 0.2 kg
v1_final ≈ 0.17 m/s
Therefore, the new velocity of the first ball after the collision is approximately 0.17 m/s.