Question

Two bars of masses and m1 and m2 connected by a non-deformed light spring rest on a horizontal plane. The coefficient of friction between the bars and the surface is equal to k. What minimum constant force has to be applied in the horizontal direction to the bar of mass m1 in order to shift the other bar?

Answer 1

$$k_{spring}x=km_2g\\Fx=0.5k_{spring}x^2+km_1gx\\F=0.5k_{spring}x+km_1g\\F=kg(m_1+0.5m_2)$$