What is the significance of sqrt{2gh} ?

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SUMMARY

The equation \(\upsilon = \sqrt{2gh}\) is significant in physics as it relates to kinetic energy (KE) and potential energy (PE), particularly in escape velocity problems and conservation of momentum applications. This equation demonstrates that when KE plus PE remains constant, it leads to equations involving \(\upsilon^2 = PE/m\), where PE can be expressed as \(mgh\). Additionally, this equation is applicable in Bernoulli's equation, which represents the conservation of energy in fluid dynamics.

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  • Understanding of kinetic energy (KE) and potential energy (PE)
  • Familiarity with Bernoulli's equation in fluid dynamics
  • Basic knowledge of conservation of momentum
  • Concept of constant acceleration in physics
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acspin
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Hi, I'm not sure how to word my question, so I will just state it upfront.

What is the importance of \upsilon = \sqrt{2gh} in physics?

I've seen it in escape velocity problems, though with an R instead of h. I've seen it with conservation of momentum applications, and it's similar to PE = mgh. Yesterday my professor was discussing Bernoulli's equation and this equation came up again.

I was just wondering how it can be applied to so many different situations...
 
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Welcome to PF!

Hi acspin! Welcome to PF! :smile:

(have a square-root: √ :wink:)

It's because v2 is KE per mass.

Whenever KE + PE =constant, you'll have equations involving v2 = PE/m, which in some cases is gh.

As to Bernouli's equation, that's just conservation of energy applied to a fluid, and both KE and PE appear in it. :smile:
 
acspin said:
What is the importance of \upsilon = \sqrt{2gh} in physics?

When acceleration is constant, say along the x-axis, then it is necessarily true that

v^2=2ax. (where v at time t=0 is zero).
 

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