Triangular vertical circle

Classical Mechanics Level 4

A rigid triangular frame is made by connecting three massless rods each of length l = 2.5 m l=\SI{2.5}{\meter} . Two point masses of mass m m each are fixed at vertices B B and C C respectively. The frame is hanging vertically from point A A about which it can rotate freely about an axis x x ’ xx’ which is perpendicular to the plane of the frame as shown in the diagram.

The point of suspension of the frame, that is A A , is accelerating with a constant acceleration a = 3 g 4 a= \frac{3g}{4} in the horizontal direction and initially frame is at rest with respect to support A A . The minimum initial angular velocity ω = x ( 3 ) 1 / 4 \omega = x(3)^{1/4} (in rad/s) provided to the system, so that it can complete vertical circular motion in the frame of support A A . Calculate the value of x x . Take g = 10 m s − 2 . g = \SI{10}{\meter \per \second \squared}.


The answer is 3.

Aarsh Verdhan by Aarsh Verdhan , 22, India

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1 solution

Aarsh Verdhan
Apr 12, 2017

If we solve in the frame of A then B and C will face a psudo force Hence there will be two torques actin on the body And the condition for completing the vertic circle will be ω ≥ 0 \omega \geq 0 when 2 m g cos ⁡ θ = 2 m a sin ⁡ θ 2mg\cos\theta=2ma\sin\theta

tan ⁡ θ = 53 d e g r e e \tan\theta=53 degree above horizontal level

Find α \alpha and integrate the ans will come out to be 3

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