In an out of control ceramics workshop, two clay balls collide in mid air and stick together. The first has mass 3.12 kg and collides with a second that is initially at rest. The composite system moves with a speed equal to one-third the original speed of the 3.12 kg ball. What is the mass of the second sphere

The mass of the second sphere is 6.24 kg.

Explanation:

Let the mass of second sphere be 'm₂' kg.

Given:

Mass of first sphere (m₁) = 3.12 kg

Initial speed of first sphere = 'u₁' (Assume)

Initial speed of second sphere (u₂) = 0 m/s

Final speed of system is one-third of 'u₁'. Let 'v' be the final speed.

So,

Now, the conservation of momentum holds true for the collision system.

Initial momentum is given as:

Final momentum is given as:

Now, from conservation of momentum, we have:

Plug in 3.12 kg for m₁ and solve for . This gives,

Therefore, the mass of the second sphere is 6.24 kg.

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