Examples of Center of Mass Motion in Real Life

📚 Quick Study Guide

🔍 The center of mass (COM) is a point that represents the average position of all the mass in a system. 💡 For a system of particles, the COM's position ($\vec{R}$) is given by: $\vec{R} = \frac{\sum m_i \vec{r_i}}{\sum m_i}$, where $m_i$ are the masses and $\vec{r_i}$ are their positions. 📝 When external forces act on a system, the COM moves as if all the mass were concentrated there and all external forces were applied there. 🏃 If there are no external forces, the velocity of the COM remains constant (even if parts of the system are moving relative to each other). 🌍 The motion of the COM is independent of the internal forces within the system. 🍎 Examples include: a diver jumping off a board, the recoil of a gun, and walking.

Practice Quiz

1. A diver jumps off a diving board. Assuming air resistance is negligible, what describes the motion of the diver's center of mass after they leave the board?
   1. It follows a straight line.
   2. It follows a parabolic path.
   3. It remains stationary.
   4. It follows a circular path.
2. A firecracker explodes in mid-air, breaking into many pieces. What happens to the center of mass of the firecracker fragments?
   1. It accelerates upwards.
   2. It falls straight down as a single particle would.
   3. It comes to an immediate stop.
   4. It explodes outwards.
3. A person walks from one end of a boat to the other on a still lake. What happens to the boat?
   1. It remains stationary.
   2. It moves in the opposite direction.
   3. It moves in the same direction.
   4. It spins in a circle.
4. A rifle fires a bullet. What describes the motion of the center of mass of the rifle-bullet system (assuming the rifle is not held by anyone and no external force)?
   1. It moves forward.
   2. It moves backward.
   3. It remains stationary.
   4. It moves up.
5. A basketball player jumps to shoot a ball. What force primarily dictates the motion of their center of mass while in the air?
   1. The force exerted by the player's muscles.
   2. Air resistance.
   3. The force of gravity.
   4. The force exerted by the ball.
6. Two ice skaters stand facing each other. One skater pushes the other. What happens to the center of mass of the two-skater system?
   1. It accelerates in the direction of the push.
   2. It accelerates in the opposite direction of the push.
   3. It remains stationary.
   4. It spins in a circle.
7. A system consists of two objects of equal mass connected by a spring. If the spring is compressed and then released, what best describes the motion of the system's center of mass?
   1. The center of mass oscillates back and forth.
   2. The center of mass moves at a constant velocity.
   3. The center of mass remains stationary.
   4. The center of mass accelerates uniformly.