Physics Explanation

This simulation demonstrates the motion of the center of mass (COM) of a system consisting of a trolley and a child.

Problem Statement: A child sits stationary at one end of a long trolley moving uniformly with speed V on a smooth horizontal floor. If the child gets up and runs about on the trolley, what is the speed of the COM of the (trolley + child) system?

Key Concepts:

• The COM velocity of a system depends only on external forces (Newton's First Law)
• Internal forces (like the child pushing on the trolley) don't affect the COM motion
• With no net external force, the COM velocity remains constant

Mathematical Explanation:

The velocity of the center of mass is given by:

v_cm = (m_trolley * v_trolley + m_child * v_child) / (m_trolley + m_child)

When the child runs:

• The child's motion creates equal and opposite internal forces on the trolley
• These forces cancel out in the COM calculation
• The COM velocity remains unchanged at its initial value

Conclusion: The child's running produces no effect on the velocity of the center of mass of the trolley-child system.