Problem # p030

FMA on system of two connected masses
Two identical masses A and B ( m = mA = mB ) are tied together by a rigid rod of length L which has negligible mass and zero mass moment of inertia. Each mass is connected to the end of the rod by a frictionless pin/hole connection.
There is no friction between mass A and the vertical wall and mass B and the horizontal floor, respectively.
Assume that m, L, and the angle Θ are given and that the masses are just released from rest ( zero velocity ).

  1. Sketch the Free-Body-Diagram for the mass A. (Hint : the rod is a 2-force member )
  2. Write out the F=ma equations ( x- and y-component) for mass A
  3. Sketch the Free-Body-Diagram for the mass B. (Hint : the rod is a 2-force member )
  4. Write out the F=ma equations ( x- and y-component) for mass B
  5. Eliminate the force of the rod from the above two equations by method of substitution to find a first equation relating the accelerations of the two masses to each other.
  6. Use the concept of relative acceleration at the time of release (when all velocities are still zero) to find a second equation relating the accelerations of the two masses to each other.
  7. Solve the two equations obtained under section 5 and 6 for the accelerations of the two masses.