SOLUTION: A billiard ball with a mass of 1.5 kg is moving at 25 m/s and strikes a second ball with a mass of 2.3 kg that is motionless. Find the velocity of the second ball if the first bal
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Question 1198186: A billiard ball with a mass of 1.5 kg is moving at 25 m/s and strikes a second ball with a mass of 2.3 kg that is motionless. Find the velocity of the second ball if the first ball stops when it strikes the
second ball.
m1 = mass of the first ball
vi1 = initial velocity of the first ball
vf1 = final velocity of the first ball
m2 = mass of the second ball
vi2 = initial velocity of the second ball
vf2 = final velocity of the second ball
Due to the elastic collision, we can use this conservation of momentum formula
m1*vi1 + m2*vi2 = m1*vf1 + m2*vf2
We have these values
m1 = 1.5 kg
m2 = 2.3 kg
vi1 = 25 m/s
vf1 = 0 m/s (since the 1st ball comes to a stop)
vi2 = 0 m/s (the 2nd ball starts at rest)
vf2 = x = unknown
Let's determine x
m1*vi1 + m2*vi2 = m1*vf1 + m2*vf2
1.5*25 + 2.3*0 = 1.5*0 + 2.3*x
37.5 = 2.3x
x = 37.5/2.3
x = 16.304347826087
x = 16
37.5 has 3 sig figs
2.3 has 2 sig figs
When dividing these items, we round to 2 sig figs since it's the smaller sig fig count.
We go for the less accurate value.
In this problem, we write the momentum conservation law in the form
= (1)
not because the collision is elastic. We write it because the momentum conservation
is the universal conservation law, which is held AT ANY COLLISION.
In this problem, the momentum conservation law is in this specific form (1),
because the second ball was at rest before the collision,
while the first ball was motionless after the collision by the condition.
From (1), we find
= , = = 16.304 m/s (rounded). ANSWER
(