PHYSICS · Multi-part · A Level · Physics · Mechanics and materials · Mechanics and materials
Problem
Four small blocks rest on a lightweight, frictionless platform that extends along the x-axis. Their initial positions (measured from the platform’s left end) and masses are:
• Block 1: 3.0 kg at x = 0.00 m
• Block 2: 1.0 kg at x = 1.00 m
• Block 3: 2.0 kg at x = 1.50 m
• Block 4: 0.50 kg at x = 2.00 m
At time t = 0, Block 3 is suddenly removed from the platform by lifting it vertically upward, so it no longer belongs to the system. No horizontal external forces act on the remaining platform–block system.
(1) Calculate the x-coordinate of the center of mass of the original four-block system just before Block 3 is removed.
(2) Determine the x-coordinate of the center of mass of the remaining three-block system immediately after Block 3 has been removed.
(3) Find the numerical value of the horizontal displacement of the center of mass of the system caused by the removal of Block 3. State whether the displacement is toward the left or toward the right relative to the platform.
(4) Explain, using principles of momentum conservation, whether any horizontal motion of the platform itself is required to keep the center of mass of the remaining system consistent with the absence of external horizontal forces.