Systems and Center of Mass
Help Questions
AP Physics C: Mechanics › Systems and Center of Mass
Based on the scenario, determine the motion of the system given its center of mass. Two pucks on frictionless ice are connected by a light string and can slide along the $x$-axis; the string tension is internal to the system. The masses are $m_1=1.0,\text{kg}$ at $x_1=-0.50,\text{m}$ and $m_2=3.0,\text{kg}$ at $x_2=+0.50,\text{m}$. A horizontal external force of $+8.0,\text{N}$ is applied to puck 1, and no other external horizontal forces act. If the system starts from rest, find the CM acceleration immediately after the force is applied.
The CM accelerates at $a_{\text{CM}}=0,\text{m/s}^2$ because tension cancels the force.
The CM accelerates at $a_{\text{CM}}=2.0,\text{m/s}^2$ to the right.
The CM accelerates at $a_{\text{CM}}=8.0,\text{m/s}^2$ to the right.
The CM accelerates at $a_{\text{CM}}=2.0,\text{m/s}^2$ to the left.
Explanation
This question tests AP Physics C Mechanics skills: systems and center of mass, specifically understanding how to determine and analyze the center of mass in physical systems. The center of mass acceleration depends only on external forces, as internal forces (like string tension) cancel out when considering the system as a whole. In this scenario, the system consists of two pucks with masses 1.0 kg and 3.0 kg connected by a string, with only an 8.0 N external force applied to the first puck. Choice B is correct because a_CM = F_ext / M_total = 8.0 N / (1.0 + 3.0) kg = 8.0 N / 4.0 kg = 2.0 m/s² to the right. Choice C is incorrect because it assumes the internal tension force somehow cancels the external force, which violates Newton's laws for system analysis. To help students: Stress that internal forces always come in action-reaction pairs that cancel when analyzing the whole system. Practice identifying and separating internal from external forces before applying Newton's second law to the center of mass.