Applied Maths - Mechanics 37
2009-08-11 9:37 pm
A mass 2m rests on a smooth horizontal table and is connected to a mass m by a light inextensible string passing through a small ring, fixed at a height h above the table. If the mass 2m is made to describe a circle of radius h/2 having its centre on the table vertically below the ring, show that the time it takes to describe the circle once is 2pi[ h (5)^0.5 /g ] ^0.5 .
回答 (1)
2009-08-12 4:23 am
✔ 最佳答案
The tension in the string is mg (which equals to the weight of the particle hung below the ring).
Let the angle between the string and the vertical be θ.
tanθ = (h/2)/h = 1/2
Resolving horizontal force,
Tsinθ = 2mω2r where r = h/2
mg(1/√5) = mω2h
ω2 = g/(√5h)
2π / Period = √ [g/(√5h)]
Period = 2π√(√5h/g)
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