Oil & Water Problem: Ball Float 50% in Water - Why Does It Rise?

AI Thread Summary
When a large amount of oil is added to water, the oil, being less dense, floats on top and pushes the water down, increasing the buoyant force acting on the ball. This causes the ball, which is initially floating 50% in water, to rise. The relevant buoyancy equation (Fb=pgB) can be applied to understand this phenomenon. Participants in the discussion emphasize the importance of Archimedes' principle in explaining the ball's behavior. Clarification on relevant equations and the density of oil compared to water is also requested to deepen the understanding of the situation.
Joe55433454
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How does a ball floating 50% in water move when a large amount of oil is added, and why?

MY Solution:

I think that the ball rises because when a large amount of oil is added, the oil sinks to the bottom causing the water to be pushed up, increasing the buoyant force which causes the ball to rise.

Relevant equations would be the buoyancy equation. Fb=pgB

Does anyone agree with me that this is right?
 
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Joe55433454 said:
How does a ball floating 50% in water move when a large amount of oil is added, and why?

MY Solution:

I think that the ball rises because when a large amount of oil is added, the oil sinks to the bottom causing the water to be pushed up, increasing the buoyant force which causes the ball to rise.

Does anyone agree with me that this is right?
Welcome to the PF.

Please do not delete the Homework Help Template when you are posting schoolwork-type problems. It is meant to help you organize your thoughts.

Part of the Template asks for the Relevant Equations. What are they in this case? Is oil heavier or lighter than water? Why do you think that a ball will float higher in oil than it will in water?
 
@berkeman

I am so sorry. I won't next time!
 
Please feel free to respond.
 
Joe55433454 said:
Please feel free to respond.
Not until you post the Relevant Equations and talk through how they could be applied here. And if you answer the other questions in my post above, that will help you work your way toward the answer.

Also, are you familiar with Archimedes' principle? :smile:
 
Thread 'Variable mass system : water sprayed into a moving container'

Thread 'Variable mass system : water sprayed into a moving container'

Starting with the mass considerations #m(t)# is mass of water #M_{c}# mass of container and #M(t)# mass of total system $$M(t) = M_{C} + m(t)$$ $$\Rightarrow \frac{dM(t)}{dt} = \frac{dm(t)}{dt}$$ $$P_i = Mv + u \, dm$$ $$P_f = (M + dm)(v + dv)$$ $$\Delta P = M \, dv + (v - u) \, dm$$ $$F = \frac{dP}{dt} = M \frac{dv}{dt} + (v - u) \frac{dm}{dt}$$ $$F = u \frac{dm}{dt} = \rho A u^2$$ from conservation of momentum , the cannon recoils with the same force which it applies. $$\quad \frac{dm}{dt}...
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