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

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In summary, the figure shows two balls racing on a track with no energy loss. The length of the dip and bump are the same. According to logic, if the curves are divided into two parts, the ball that travels upwards will last longer than the one traveling downwards. Therefore, the bump ball will have a higher speed and will complete the second part of the curve in less time than the other ball. This can be proved using science and intuition. Ultimately, the ball that reaches the bottom of the dip faster, which is A, will win the race. This is due to the fact that the average speed of A in the dip is greater than the average speed of B over the bump.
  • #1
sa_ta
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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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  • #2
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 :)
 
  • #3
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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  • #4
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.
 
  • #5
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?"
 
  • #6
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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  • #7
so, from ur explanation A and B wins and reach at the same time?
:confused:
 
  • #8
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.
 
  • #9
thanks a lot
now i understand what did u mean
 

1. How can I use Bernoulli's rule to solve for pressure in a fluid?

To use Bernoulli's rule to solve for pressure in a fluid, you will need to know the height and velocity of the fluid at different points. Using the equation P + (1/2)ρv^2 + ρgh = constant, where P is pressure, ρ is density, v is velocity, g is the acceleration due to gravity, and h is the height, you can solve for pressure at any given point.

2. Can Bernoulli's rule be applied to non-ideal fluids?

Yes, Bernoulli's rule can be applied to non-ideal fluids, but it may require additional factors to be considered, such as viscosity and turbulence. In these cases, the equation may need to be modified to account for these factors.

3. How is Bernoulli's rule used in real-world applications?

Bernoulli's rule is used in various real-world applications such as aircraft and car design, hydraulic systems, and fluid mechanics. It is also used in weather prediction and aerodynamic studies.

4. What are the limitations of Bernoulli's rule?

Bernoulli's rule assumes that the fluid is incompressible, non-viscous, and irrotational. In reality, most fluids do not meet these criteria, so the rule may not accurately predict real-world scenarios. Additionally, Bernoulli's rule only applies to steady-state, or constant, flows.

5. What are some common misconceptions about Bernoulli's rule?

One common misconception about Bernoulli's rule is that it explains how airplanes can fly. While it does play a role in aerodynamics, it is not the only factor in flight and cannot fully explain the phenomenon. Another misconception is that Bernoulli's rule only applies to liquids. However, it can also be applied to gases as long as the fluid is incompressible and non-viscous.

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