Center of Mass - AP Physics 1: Unit 2 Review Supplement

Summary

This AP Physics 1 review session delves into two key center of mass problems. The first explores the effect of a person climbing down a rope hanging from a helium balloon, emphasizing equilibrium and the constancy of the system's center of mass. The second problem addresses an ice skater throwing a book, demonstrating conservation of momentum in a frictionless environment. Both problems highlight the principle that, with no external forces, the center of mass either remains at rest or moves with constant velocity, offering valuable insights into fundamental physics principles relevant for the AP Physics 1 exam.

Takeaways

• 😀 The video focuses on two center of mass multiple-choice problems to review for the AP Physics 1 exam.
• 😀 The first problem involves a balloon-person system in equilibrium, with a massless rope hanging from it.
• 😀 The key point in the first problem is that the center of mass of the system remains in the same place relative to the Earth throughout the person's movement on the rope.
• 😀 The center of mass of the balloon-person system is initially at a distance of R from the center of mass of both objects, and moves to a distance of 2R after the person climbs to the bottom of the rope.
• 😀 A critical assumption in the problem is that the rope is massless, meaning it doesn't affect the system's center of mass.
• 😀 In the second problem, the person throws their physics textbook while sliding on frictionless ice, creating a momentum transfer between them and the book.
• 😀 The system's total linear momentum is conserved during the explosion (the throwing of the book), as there is no external force acting on the system.
• 😀 The velocity of the center of mass of the system before and after the book is thrown remains the same due to the conservation of momentum, despite the person's change in motion.
• 😀 The second problem requires understanding two-dimensional conservation of momentum, but the answer ultimately simplifies to the fact that the center of mass remains at a constant velocity.
• 😀 The key lesson in both problems is that when there is zero net external force on the system, the center of mass will either stay at rest or continue with constant velocity, depending on the scenario.

Q & A

What does the center of mass of the balloon-person system do when the person climbs down the rope?

The center of mass of the balloon-person system stays in the same position relative to the Earth, because there are no external forces acting on the system, and the system remains in equilibrium.

Why is it assumed that the rope has no effect on the center of mass of the system?

The problem specifically states that the rope is massless, which means it does not contribute to the overall mass of the system and therefore does not affect the center of mass.

In the first problem, why does the center of mass of the balloon-person system shift as the person moves?

The center of mass shifts because the relative position between the balloon and the person changes as the person climbs, but the overall center of mass stays the same relative to the Earth due to the system’s equilibrium.

What does the term 'net external force' mean in the context of these problems?

A net external force refers to any force acting on the system from outside. If there is no net external force (as in these problems), the center of mass will either stay at rest or maintain constant velocity, depending on the system’s initial conditions.

Why is the velocity of the center of mass of the system constant after the person throws the book in the second problem?

The velocity of the center of mass remains constant because there are no external forces acting on the system during the 'explosion' of throwing the book. This is a key principle of the conservation of momentum.

How is momentum conserved in the second problem when the person throws the book?

Momentum is conserved because the total momentum of the system (person + book) before and after the throw remains the same. Since there is no external force, the total momentum before and after the throw must be equal.

What is the role of the mass of the person compared to the mass of the book in the second problem?

The mass of the person is 40 times the mass of the book, which affects the velocity of the center of mass. However, the center of mass still moves with a constant velocity, reflecting that there’s no external force to change the system’s momentum.

In the first problem, why does the center of mass initially sit halfway between the two objects?

The center of mass initially sits halfway between the two objects because both objects (the balloon and the person) have the same mass, so the center of mass is equidistant from each object.

How does the concept of equilibrium apply to the first problem?

In the first problem, equilibrium means that the forces acting on the system are balanced, and as a result, the system’s center of mass does not move relative to the Earth. The system remains at rest throughout.

What insight does the second problem provide about solving complex physics questions?

The second problem highlights that when facing complex problems, it’s important to recognize when simpler concepts, like conservation of momentum or the constancy of the center of mass, can simplify the solution. This can help avoid unnecessary complex calculations.