Answered

If the hoop has speed vo at the bottom of
the pipe, what is its speed when it has rolled
halfway up the side of the pipe?

If The Hoop Has Speed Vo At The Bottom Of The Pipe What Is Its Speed When It Has Rolled Halfway Up The Side Of The Pipe class=

Answer :

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ONYEBUCHINNAJIGO

The speed of the hoop when it has rolled halfway up the side of the pipe is √(v₀² - gR).

Conservation of energy

The speed of the hoop when it has rolled halfway up the side of the pipe is calculated as follows;

K.E = P.E

- ¹/₂mv₀²  + ¹/₂Iω² = (mgh₀ - mghf)

- ¹/₂mv₀²  + ¹/₂Iω² = (0 - 0.5mgh)        (hf = 0.5h) (half way up)

¹/₂Iω² = ¹/₂mv₀² - 0.5mgh  

where;

  • I is moment of inertia of the hoop = mr²
  • ω is angular speed = v/r

¹/₂(mr²)(vf/r)² = ¹/₂mv₀²  - 0.5mgh

¹/₂vf²  = ¹/₂v₀² - ¹/₂gh  

vf²  = v₀² - gh

vf = √(v₀² - gh)

where;

  • h is the distance traveled half-way up the pipe = R

vf = √(v₀² - gR)

[tex]v_f = \sqrt{v_0^2 - gR}[/tex]

Learn more about moment of inertia of hoop here: https://brainly.com/question/14956994

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