Question
Two frictionless blocks of equal masses m are connected by a massless rigid rod of length L. The system is constrained to move in the vertical plane under the action of an applied force as shown in the figure. Obtain the equation of motion of the system and calculate the condition for static equilibrium.
Answer :
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Skip in 10
Consider two blocks of equal mass (m) connected by a massless rigid rod of length (L) moving in a vertical plane. Let the positions of the two blocks be described by coordinates ((x_1, y_1)) and ((x_2, y_2)). Since the rod is rigid and massless, the constraint is given by [ (x_2 - x_1)^2 + (y_2 - y_1)^2 = L^2. ] Let an external force (F(t)) act on one of the blocks. Using Lagrangian mechanics, the kinetic energy of the system is [ T = \frac{1}{2}
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