M3 question ex4d question 1 Watch

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Lucky Penny
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#1
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Help help help

A glass marble of mass m is moving in a horizontal circle round the inside surface of a smooth hemisperical bowl o fradius r. The centre of the circle is at a distance r/2 below the centre of the bowl. State a suitable model for the marble and hence find the magnitude of the reaction between the marble and the bowl and the speed of the marble.

NO IDEA?!
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Sparkling_Jules
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Maybe do it like a conical pendulum? Instead of tension in the string, reaction form the bowl? This stumped me and I just left it...
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Lucky Penny
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what a strange question.. not sure if the reaction is then perpendicular to the bowl which just wouldn't make sense.. god so don't need this night before the bloody exam!
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Christophicus
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oh, I did this ages ago. it took me about a page.
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Sparkling_Jules
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It works!!! Wait a mo and I'll right up...
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Sparkling_Jules
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First off: cos a = (r/2 / r) = ½
a = 60°

^ vertically: Rcos60 = mg
½R = mg
R = 2mg

< horizontally: mv²/rsin60 = Rsin60

divide < by ^: Rsin60/Rcos60 = mv²/mgrsin60

tan60 = v²/(√3/2)gr
v² = (√3√3)gr/2
v² = 3gr/2
v = √(3gr/2)
v = √¼√(6gr)

v = 2√(6gr)


Yay! Can't believe I finally got that!
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