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Grade 11Mechanics

A cylinder of weight w is resting on a fixed V groove whose angles with horizontal are 60 degrees each. Calculate the normal reactions between the cylinders and two inclined walls.

Saurabh

8 Years agoGrade 11

1 Answer

Arun

8 Years ago

Cylinder in V groove.

Let us assume that the angles A made by inclined surface in groove with the vertical are both same. Let the cylinder rest symmetrically in the groove. Surface ST is horizontal. Normal reactions are N1 and N2. Also, frictions f1 and f2 are equal if the groove surface is of same kind on both sides.
The cylinder is in a static equilibrium. Balance forces in vertical direction and horizontal direction.
N1 cos A - f 1 Sin A - N2 Cos A + f2 sin A = 0
=> (N1- N2) Cos A = (f1-f2) Sin A --- (1) f1
moments of the forces wrt Q: SQ * N1 = QT * N2 => N1/ N2 = QT / SQ --- (3)
Substitute in (2) to get: N2 (1+ QT/SQ) = W / (sin A + mu Cos A) N2 = W *QS /[( sinA + mu Cos A) (Qs+QT) ] N1 = W * QT / [( sinA + mu Cos A) (Qs+QT) ]
If QS = QT then, N = W / [ 2 (sin A + mu Cos A) ]

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