A 0.600-kg ball traveling 4.00 m/s to the right collides with a 1.00-kg ball traveling
5.00 m/s to the left. After the collision, the lighter ball is traveling 7.25 m/s to the
left. What is the velocity of the heavier ball after the collision?
A 0.600-kg ball traveling 4.00 m/s to the right collides with a 1.00-kg ball traveling
5.00 m/s to the left. After the collision, the lighter ball is traveling 7.25 m/s to the
left. What is the velocity of the heavier ball after the collision?
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.
Let's define the positive direction as to the right and the negative direction as to the left.
The momentum of an object is given by the product of its mass and velocity. Therefore, the momentum before the collision can be calculated as:
Momentum_before = (mass of the 0.600-kg ball * velocity of the 0.600-kg ball) + (mass of the 1.00-kg ball * velocity of the 1.00-kg ball)
Momentum_before = (0.600 kg * 4.00 m/s) + (1.00 kg * (-5.00 m/s)) [as the velocity of the 1.00-kg ball is to the left]
Momentum_before = (2.40 kg·m/s) + (-5.00 kg·m/s)
Momentum_before = -2.60 kg·m/s
The momentum after the collision can be calculated similarly:
Momentum_after = (mass of the 0.600-kg ball * velocity of the 0.600-kg ball) + (mass of the 1.00-kg ball * velocity of the 1.00-kg ball)
Momentum_after = (0.600 kg * (-7.25 m/s)) + (1.00 kg * velocity of the heavier ball)
Now, since momentum is conserved, we can equate the momentum before and after the collision:
Momentum_before = Momentum_after
-2.60 kg·m/s = (0.600 kg * (-7.25 m/s)) + (1.00 kg * velocity of the heavier ball)
Solving for the velocity of the heavier ball, we get:
velocity of the heavier ball = (-2.60 kg·m/s - (0.600 kg * (-7.25 m/s))) / 1.00 kg
velocity of the heavier ball = (-2.60 kg·m/s + 4.35 kg·m/s) / 1.00 kg
velocity of the heavier ball = 1.75 m/s
Therefore, the velocity of the heavier ball after the collision is 1.75 m/s.