Finding velocity of lump of clay. (Not too sure on answer)

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The problem involves two lumps of clay, each weighing 3.5 kg, colliding on frictionless ice, with one moving at 4.8 m/s to the right and the other at 2.3 m/s to the left. After applying the conservation of momentum equation, the final velocity of the combined mass is calculated to be 1.25 m/s to the right. It is confirmed that kinetic energy is not conserved during the collision, but the numerical change in kinetic energy should be calculated to show whether it increased or decreased. The direction of the final velocity is crucial for clarity. Overall, the discussion emphasizes the importance of both momentum conservation and kinetic energy analysis in collision problems.
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Homework Statement


Two lumps of clay, each with the same mass 3.5 kg, are sliding on ice, with no friction. One is moving at 4.8 m/s to the right, the other is moving at 2.3 m/s to the left. They collide and stick to one another. Calculate the velocity of the lump of clay after the collision. Is the total kinetic energy constant?

Homework Equations


(m1+m2)vf=m1v1+m2v2

The Attempt at a Solution


Substituted m1 and m2=3.5 kg, v1=-2.3 m/s, and v2=4.8 m/s. With that, I got vf=1.25 m/s. I'm almost sure that one of the velocity is negative since one lump of clay is moving in the opposite direction away from the other. For the second question of whether or not total kinetic energy is constant, I said no.
 
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fantisism said:

Homework Statement


Two lumps of clay, each with the same mass 3.5 kg, are sliding on ice, with no friction. One is moving at 4.8 m/s to the right, the other is moving at 2.3 m/s to the left. They collide and stick to one another. Calculate the velocity of the lump of clay after the collision. Is the total kinetic energy constant?

Homework Equations


(m1+m2)vf=m1v1+m2v2

The Attempt at a Solution


Substituted m1 and m2=3.5 kg, v1=-2.3 m/s, and v2=4.8 m/s. With that, I got vf=1.25 m/s. I'm almost sure that one of the velocity is negative since one lump of clay is moving in the opposite direction away from the other. For the second question of whether or not total kinetic energy is constant, I said no.
The final speed is correct, but you should state, what is the direction of it.
Yes, the kinetic energy is not conserved, but you should show its numerical value. Did it increased or decreased with respect to the initial one?
 
The book claims the answer is that all the magnitudes are the same because "the gravitational force on the penguin is the same". I'm having trouble understanding this. I thought the buoyant force was equal to the weight of the fluid displaced. Weight depends on mass which depends on density. Therefore, due to the differing densities the buoyant force will be different in each case? Is this incorrect?

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