Throwing a Ball in a Boat - Demonstrating Center of Mass

Summary

In this educational demonstration, Mr. P and his students explore Newton's Laws through a scenario where a ball is thrown in or out of a canoe. They discuss the behavior of the system's center of mass and the effects of internal and external forces. When the ball lands in the canoe, everything stops moving to keep the center of mass stationary. However, when the ball lands outside, the canoe continues to move due to an external force. Through calculations and explanations, they clarify the relationship between motion, force, and center of mass, all while keeping the physics principles intact.

Takeaways

• 😀 Newton's Third Law: Internal forces within a system do not affect the overall motion of the system.
• 😀 Center of Mass: The center of mass of a system remains at rest relative to the Earth when no external force acts on it.
• 😀 System Definition: The system includes all objects that are considered in the analysis (e.g., the canoe, the ball, and Mr. P).
• 😀 No Net External Force: If there is no external force acting on a system, the system will not accelerate.
• 😀 Forces in Projectile Motion: While the ball is in projectile motion, the canoe and Mr. P move to the right as the ball moves to the left.
• 😀 Conservation of Center of Mass: The system's center of mass does not move relative to the Earth, so any movement in one part of the system is balanced by movement in another part.
• 😀 Internal Forces: Forces between the ball and Mr. P (and between the ball and the canoe) are internal to the system, so they do not cause the system to accelerate.
• 😀 Ball Landing in Canoe: When the ball lands in the canoe, the system's center of mass stops moving, and both the ball and the canoe cease to move.
• 😀 External Forces and Continued Motion: If the ball lands outside the canoe, it is no longer part of the system, and external forces cause the canoe and Mr. P to continue moving to the right.
• 😀 Calculating the Change in Position: The change in the position of the center of mass is calculated using the masses and positions of the objects involved, leading to the conclusion that the center of mass moves 15 cm to the left.

Q & A

Why does the canoe and Mr. P move to the right when the ball is thrown to the left?

According to Newton's Third Law, when Mr. P applies a force on the ball to throw it to the left, the ball applies an equal but opposite force on Mr. P and the canoe, causing them to move to the right. This is because the system is initially at rest, and the forces involved are internal to the system, meaning the center of mass of the system remains in place relative to the Earth.

Why does everything stop moving when the ball lands in the canoe?

When the ball lands in the canoe, there is no longer any external force acting on the system (ball, canoe, and Mr. P). As a result, the system does not accelerate, and the center of mass of the system must stay at rest relative to the Earth. The internal forces between the ball and the canoe cause them to stop moving, ensuring the center of mass remains stationary.

What does it mean for the system to have no net external force acting on it?

If there is no net external force acting on the system, it means that all forces involved are internal (between the objects in the system). As a result, the system does not experience any acceleration or change in velocity. The center of mass of the system will remain in the same location relative to Earth.

How is the center of mass of the system affected when the ball moves to the left?

As the ball moves to the left, the center of mass of the system also shifts to the left relative to the canoe. However, since the system is isolated (no external forces), the center of mass must stay stationary relative to the Earth, so the canoe and Mr. P must move to the right to keep the center of mass in the same location relative to Earth.

Why does the ball's motion cause the canoe and Mr. P to move in the opposite direction?

When the ball moves to the left, it displaces part of the system, shifting the center of mass. To compensate for this displacement, the canoe and Mr. P must move to the right to ensure that the center of mass of the entire system stays in the same position relative to the Earth.

What happens if the ball lands outside the canoe?

If the ball lands outside the canoe, the system now only includes the canoe and Mr. P. Since the ball is no longer part of the system, an external force is applied to the canoe and Mr. P, causing them to continue moving to the right at a constant velocity. This differs from the case where the ball lands inside the canoe, where no external force acts on the system.

Why is the ball not considered part of the system if it lands outside the canoe?

The ball is no longer part of the system because it has left the canoe and is no longer interacting with the canoe and Mr. P in the same way. When the ball leaves the system, the forces it exerts on the canoe and Mr. P are no longer internal to the system, and therefore, an external force acts on the remaining system (canoe and Mr. P).

How does the calculation of the center of mass help explain the movement of the system?

The calculation of the center of mass shows how the mass distribution of the system affects its overall motion. By comparing the initial and final positions of the center of mass, we can determine how much the system must move to maintain its center of mass in the same location relative to Earth, as demonstrated by the 15 cm shift in the example.

What is the significance of the zero reference point in this experiment?

The zero reference point is set at the center of the canoe, which allows all measurements of positions to be relative to the canoe. This simplifies the calculations and helps track the movement of the center of mass in a consistent way, as all other positions are measured relative to this fixed point.

What does 'delta' represent in the context of the center of mass calculation?

'Delta' represents the change in position of the center of mass. It is calculated as the final position of the center of mass minus the initial position. In this case, the center of mass moved 15 cm to the left relative to the canoe, which explains why the canoe moved 15 cm to the right to maintain the system’s overall center of mass relative to Earth.