(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

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?

2. Relevant equations

ƩF=[itex]\frac{mv^{2}}{r}[/itex] ....(1)

Ncosθ=mg ...(2)

3. 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{v^{2}}{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' = (r^{2}-([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 :!!)

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# Homework Help: Circular motion in hemisphere

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