Three point masses rest on a smooth horizontal table
PHYSICS · Multi-part · AP · Physics 1: Algebra-based · Force and Translational Dynamics · Force and Translational Dynamics
Problem
Three point masses rest on a smooth horizontal table, forming an L-shaped configuration:
• Mass 1: 2 kg located at (0 m, 0 m)
• Mass 2: 3 kg located at (4 m, 0 m)
• Mass 3: 1 kg located at (4 m, 3 m)
The positive x-axis points to the right and the positive y-axis points upward.
A frictionless groove allows Mass 3 to slide straight downward along the line x = 4 m until it meets Mass 2. When they come into contact, the two masses lock together and continue to move as a single object of combined mass 4 kg located at (4 m, 0 m). No external horizontal forces act during the motion.
(a) Calculate the coordinates (x, y) of the center of mass of the three-mass system before Mass 3 begins to slide.
(b) Determine the coordinates of the center of mass of the system after Mass 3 has locked onto Mass 2.
(c) Compute the displacement vector of the system’s center of mass between the initial and final moments. Express both the magnitude and the angle the vector makes with the positive x-axis.
(d) Explain why your numerical result in part (c) is consistent with fundamental conservation principles, and discuss how redefining sub-systems (the locked pair versus separate masses) influences your intermediate calculations but not the final conclusion.