A 3.20 kg mud ball has a perfectly inelastic collision with a second mud ball that is initially at rest. The composite system moves with a speed equal to one-half the original speed of the 3.20 mud ball. What is the mass of the second mud ball?
kg
To solve this problem, we can use the principle of conservation of momentum.
The principle of conservation of momentum states that the total momentum of a system of objects remains constant if no external forces act on it. In this case, since the mud balls are the only objects in the system and assuming no external forces are present, we can apply this principle.
Let's define the following variables:
m1: mass of the first mud ball (3.20 kg)
v1: original velocity of the first mud ball
m2: mass of the second mud ball
v2: final velocity of the composite system (which is one-half the original velocity of the first mud ball)
According to the conservation of momentum, the total momentum before the collision is equal to the total momentum after the collision.
Before the collision, the momentum of the first mud ball is given by:
m1 * v1
After the collision, the momentum of the composite system is given by:
(m1 + m2) * v2
Since the composite system moves with a speed equal to one-half the original speed of the 3.20 mud ball, we have:
v2 = 0.5 * v1
Applying the conservation of momentum, we can equate the momentum before and after the collision:
m1 * v1 = (m1 + m2) * v2
Substituting v2 = 0.5 * v1:
m1 * v1 = (m1 + m2) * (0.5 * v1)
Now, let's solve the equation to find the mass of the second mud ball (m2).
m1 * v1 = (m1 + m2) * (0.5 * v1)
m1 * v1 = 0.5 * (m1v1 + m2v1)
2m1v1 = m1v1 + m2v1
m1v1 = m2v1
m2 = m1
Therefore, the mass of the second mud ball is equal to the mass of the first mud ball, which is 3.20 kg.