03 Student’s Centre of Mass

03 Student’s Centre of Mass#

Aim#

To show that the centre of mass (\(CM\)) will not move when only internal forces act.

Subjects#

  • 1D40 (Motion of the Center of Mass)

Diagram#

../../../../../_images/figure_03.png

Fig. 15 .#

Equipment#

  • Two light carts (skateboards), easy rolling.

  • Rope, \(l=10\mathrm{~m}\).

  • Light student.

  • Heavy student.

Presentation#

The two carts are positioned at the front of the lecture hall—one on the right side, the other on the left. Two student volunteers each stand on a cart, holding opposite ends of a rope. Knowing the students’ masses, the \(CM\) can be determined, and this position is marked on the floor. When one or both students gently pull on the rope, the carts move toward each other and meet approximately at the \(CM\).

Explanation#

Explanation: The CM of a system of particles represents the average position of those particles. So, seen from the CM:

\[m_{1} r_{1}+m_{2} r_{2}+\ldots=0\]

The larger the mass \((m)\), the smaller \(r\) will be. Since no external forces are acting, the CM will not be displaced, as this demonstration verifies.

Sources#

  • Mansfield, M and O’Sullivan, C., Understanding physics, pag. 128

Contents