How do I solve problems involving conservation of momentum?

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To solve problems involving conservation of momentum, it's essential to understand that the total initial momentum of a system must equal the total final momentum. This can be expressed mathematically as the sum of the products of mass and velocity for all objects before the event equaling the sum after the event. When setting up a problem, identify all objects involved and their respective masses and velocities. Use the equation (massA)(velocityA) + (massB)(velocityB) = (massA)(velocityA) + (massB)(velocityB) to solve for unknowns. Mastering this concept is crucial for accurately analyzing momentum-related problems.
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i am confused on how to set up a problem involving initial and final momentum . . . please help
 
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What's your problem? Does this have to do with the conservation of momentum?
 
Conservation of Momentum. Initial momentum must equal final momentum. Therefore...

(mass)x(velocity) = (mass)x(velocity)

or...

(massA)x(velocityA) + (massB)x(velocityB) ... (massX)x(velocityX) =
(massA)x(velocityA) + (massB)x(velocityB) ... (massX)x(velocityX)
 

Thread 'Magnitude of buoyant force in fluids of different densities'

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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