Question

In a perfectly inelastic collision, a 2.70 kg mud ball collides with a second mud ball initially at rest, and the composite system moves with a speed equal to one-fourth the original speed of the 2.70 kg mud ball. What is the mass of the second mud ball?

Answer 1

Using the law of conservation of momentum for a perfectly inelastic collision, where the total momentum before impact is equal to the total momentum after impact, the mass of the second mud ball was calculated to be 2.025 kg.

Step-by-step explanation:

In the scenario of a perfectly inelastic collision, we have a known mass (2.70 kg) colliding with an unknown mass, and after the collision, they move together with a speed that is one-fourth of the initial speed of the known mass. We can use the conservation of momentum to solve for the unknown mass. The formula for momentum is p = mv, where p is momentum, m is mass, and v is velocity.

Let m1 = 2.70 kg (mass of the first mud ball), v1 = initial velocity of m1, m2 = mass of the second mud ball (which we want to find), and v2 = 0 (since the second mud ball is initially at rest). After the collision, the new velocity v' = v1/4. According to conservation of momentum, the total momentum before the collision equals the total momentum after the collision:

m1 * v1 + m2 * v2 = (m1 + m2) * v'

By substituting v2 with 0 and v' with v1/4, and rearranging the formula, we can find the mass of the second mud ball m2:

m2 = (3 * m1) / 4

Plugging in the known values, we get:

m2 = (3 * 2.70 kg) / 4

m2 = 2.025 kg

Therefore, the mass of the second mud ball is 2.025 kg.