Which Ball Wins the Race According to Bernoulli's Principle?

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In the discussion about which ball wins the race according to Bernoulli's Principle, it is concluded that Ball A will win due to its faster average speed in the dip compared to Ball B's slower speed on the bump. The analysis indicates that while both balls experience the same energy dynamics, Ball A gains speed as it descends and maintains a higher average speed throughout the course. The key point is that the time taken by Ball A to navigate the dip is less than the time taken by Ball B to ascend the bump. Therefore, despite both paths being equal in length, Ball A completes the race first. The conclusion emphasizes the importance of speed variations in different sections of the track.
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http://up2.up-images.com/up//uploads2/images/hosting-036ee42f15.jpg

in the figure, which ball will win in the race?
note: there is no energy loss
 
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You can use logic to solve it. For example provided curves are the same (obvious) divide them into two parts, then its clear that the upwards one will last more than the downwards and then the bump ball will have speed so it'll need less time tha the other to complete the second part of the curve. This is what my intuition tells me but I think that it can be proved I do I tell you.

Good science :)
 
sa_ta said:
http://up2.up-images.com/up//uploads2/images/hosting-036ee42f15.jpg

in the figure, which ball will win in the race?
note: there is no energy loss

Hello sa ta.You have already given the answer.If there is no energy loss what does that tell you?
 
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Length of dip and bump is the same.
But A moves faster in the dip and B moves slower on the bump. So A wins the race.
 
thanks for all .. but i need the right answr today please??
A or B wins the race? and why??

Dadface: can u answer ur question "If there is no energy loss what does that tell you?"
 
There is a KE to KE change as the balls cross the bump and the hill. The KE gained by A on the way down is lost on the way up and the KE lost by B on the way up is gained on the way down,from this we conclude that the balls travel with the same steady speed on the flat portions.Now consider the average speed of the balls on the bump and in the dip as explained by ri.bhat,for example why does A get to the bottom of the dip faster than B gets to the top of the hill?What can you then say about the average times for the whole journey?
 
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so, from ur explanation A and B wins and reach at the same time?
:confused:
 
No, A wins.Consider the change of speed of A as it moves to the bottom of the dip and then rises to the top again .Now consider the change of speed of B as it rises to the top of the bump and then falls.Now compare the two and you should see that the average speed of A in the dip is greater than the average speed of B over the bump.
 
thanks a lot
now i understand what did u mean
 

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