A uniform thin metal plate is shaped like an upright capital "T" made by welding two…
PHYSICS · Multi-part · AP · Physics 1: Algebra-based · Force and Translational Dynamics · Force and Translational Dynamics
Problem
A uniform thin metal plate is shaped like an upright capital "T" made by welding two rectangles together:
• Cross-bar: 0.30\,m wide and 0.04\,m thick.
• Stem: 0.12\,m wide and 0.50\,m tall, attached centrally under the cross-bar so that their centerlines coincide.
The density and thickness of the metal are uniform. A coordinate system is placed with its origin at the geometric center of the cross-bar, the x–axis horizontal, and the y–axis vertical (positive upward).
(a) Using symmetry, state the x–coordinate of the plate’s center of mass and justify your answer briefly.
(b) Calculate the y–coordinate of the center of mass relative to the origin.
(c) Express the depth below the top surface of the cross-bar at which the center of mass lies.