Two point-like packages

PHYSICS · Multi-part · AP · Physics 1: Algebra-based · Force and Translational Dynamics · Force and Translational Dynamics

Problem

Two point-like packages, m1=2.0 kgm_1 = 2.0\,\text{kg} and m2=5.0 kgm_2 = 5.0\,\text{kg}, rest on a smooth horizontal warehouse floor. Initially, m1m_1 is located at the origin and m2m_2 is located at (3.0 m, 0)(3.0\,\text{m},\,0). A worker pushes only on m1m_1, sliding it straight along the xx-axis to the point (6.0 m, 0)(6.0\,\text{m},\,0). Treat the floor as frictionless and neglect all other forces except those exerted by the worker. (1) Calculate the coordinates of the center of mass of the two-package system before the worker moves m1m_1. Express your answer in meters. (2) Calculate the coordinates of the center of mass of the system after m1m_1 reaches (6.0 m,0)(6.0\,\text{m},0). Express your answer in meters. (3) Determine the displacement vector of the center of mass of the system caused by the worker’s action. Give both magnitude and direction relative to the positive xx-axis.

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