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IIK*JII
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Homework Statement
As shown in attached figure, a small object is in uniform circular motion in a horizontal plane, on the smooth of a hemisphere (radius:r). The distance between the object's plane of motion and the hemisphere's lowest point is [itex]\frac{r}{5}[/itex]
What is the speed of the object?
Homework Equations
ƩF=[itex]\frac{mv2}{r}[/itex] ...(1)
Ncosθ=mg ...(2)
The Attempt at a Solution
From (1)
and I get ƩF from FBD wrote in attached figure ƩF=Nsinθ
From (2) I knew that N=[itex]\frac{mg}{cosθ}[/itex] ..(3)
substitute (3) in (1) in got gtanθ=[itex]\frac{v2}{r}[/itex] ..(4)
and I try to find tanθ from geometric of hemisphere
First, I try to find the radius (let it is r') of this mass at r/5 from the lowest point of hemisphere
If I look in the picture and use pythagoras r' = (r2-([itex]\frac{4r}{5}[/itex]))1/2
∴r' = [itex]\frac{3r}{5}[/itex]
Thus; tanθ = 3
substitute in (4) v = √3gr
but the answer is [itex]\frac{3√5gr}{10}[/itex]...
Or I get tanθ wrong or use wrong geometric condition of hemisphere ?
help is appreciate
Thanks :!)