Question

Two rigidly connected homogeneous rods of the same length and mass m₁ and m₂ respectively form an angle pi/2 and rest on a rough horizontal surface (Fig. 23). The system is uniformly pulled with the help of a string fixed to the vertex of the angle and parallel to the surface.

Determine the angle a formed by the string and the rod of mass m₁.

Answer 1

After the translatory motion of the system has been established, the ratio of the forces of friction F_fr1 and F_fr2 acting on the first and second rods will be equal to the ratio of the forces of pressure of the corresponding regions: F_fr1/F_fr2 = N₁/N₂. Since each force of pressure is proportional to the mass (N₁ = m₁g and N₂ = m₂g), the ratio of the forces of friction can be written in the form

On the other band, from the equality of the moments of these forces about the vertex of the right angle (Fig. 158, top view), we obtain

where l is the distance from the vertex to the centres of mass of the rods. From Eqs. (1) and (2), we obtain

Consequently