Question

A 3.14 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-eighth the original speed of the 3.14 mud ball. what is the mass of the second mud ball?

Answer 1

To find the mass of the second mud ball in a perfectly inelastic collision where the combined system's speed is one-eighth of the initial speed, we use the conservation of momentum. The mass of the second mud ball is calculated to be 24.96 kg.

Step-by-step explanation:

The student's question refers to a problem involving a perfectly inelastic collision where a mud ball of mass 3.14 kg, moving with an initial speed, collides with a second stationary mud ball. After the collision, the two mud balls stick together and move with a speed that is one-eighth of the original speed of the 3.14 kg mud ball. To find the mass of the second mud ball, we can use the principle of conservation of momentum. The momentum before the collision must equal the momentum after the collision since no external forces are acting on the system.

Let's denote the mass of the second mud ball as m. The initial momentum of the system is given by the momentum of the 3.14 kg mud ball, which is its mass times its velocity (p_initial = 3.14 kg × v). The final momentum of the system is the total mass times the final velocity (p_final = (3.14 kg + m) × ⅛v, where ⅛ represents one-eighth). Setting these equal for conservation of momentum, we get:

3.14 kg × v = (3.14 kg + m) × ⅛v

Solving for m gives us m = (3.14 kg × v - ⅛ × 3.14 kg × v) / ⅛v = 3.14 kg × (1 - ⅛) / ⅛

The mass of the second mud ball, m, is therefore 3.14 kg × (7/8) / (1/8) = 24.96 kg.