'Iwo blocks of masses m1 and m2 connected by a light spring...

'Iwo blocks of masses $m_{1}$ and $m_{2}$ connected by a light spring of stiffiness $k$ as shown in figure rest on a smooth horizontal plane. Block 2 is shifted a small distance $x$ to the left and then released. Find the velocity of the centre of mass of the system after block 1 breaks off the wall.

Key Concepts

Spring-Mass System Dynamics

Spring-mass systems involve masses connected by springs that can exert restoring forces leading to oscillatory behavior. Analyzing such systems requires understanding how elastic forces interact with the masses, and although these forces can alter the relative positions and velocities of the masses, they do not change the velocity of the center of mass if there are no unbalanced external forces.

Center of Mass

The center of mass of a system is the weighted average position of all the mass in the system. It is an important concept because, under the influence of only internal forces, the center of mass will continue in uniform motion (or remain at rest) according to Newton’s first law, regardless of the internal dynamics between the parts.

Conservation of Linear Momentum

In the absence of external forces, the total linear momentum of a system remains constant. This principle is crucial when analyzing problems involving internal forces, such as those provided by a spring, because the motion of the center of mass is determined solely by any net external forces acting on the system.

Internal versus External Forces

Understanding the difference between internal and external forces is key when studying systems of particles. Internal forces, like the spring force connecting two masses, can change the individual motions of the parts but do not affect the overall motion (momentum) of the center of mass, whereas external forces change the system’s total momentum.

Please give Ace some feedback