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Chapter 1: Problem 2

A body falling vertically downwards under gravity breaks in two parts of unequal masses. The centre of mass of the two parts taken together shifts horizontally towards: (1) heavier piece (2) lighter piece (3) does not shift horizontally (4) depends on the vertical velocity at the time of breaking

Short Answer

Expert verified
The center of mass does not shift horizontally (Option 3).

Step by step solution

01

Understand the Problem Statement

We have a body falling straight down due to gravity, which means initially, there is no horizontal motion. At some point, it breaks into two pieces of unequal mass. The problem asks how the center of mass behaves horizontally after breaking.
02

Apply Conservation of Momentum

According to the law of conservation of linear momentum, the total momentum of an isolated system remains constant in the absence of external forces. Initially, there is no horizontal momentum because the body is only moving vertically. Since no external horizontal forces are acting on it, the horizontal momentum must remain zero throughout.
03

Analyze Horizontal Motion of Center of Mass

For the center of mass to shift horizontally, there would have to be some net horizontal motion or force. However, since the initial horizontal momentum is zero and no external horizontal forces act on the system, the center of mass cannot have horizontal motion. Therefore, the center of mass does not shift horizontally.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Conservation of Momentum
The concept of conservation of momentum is a fundamental principle in physics. It states that the total momentum of a closed system remains constant if no external forces act on it. In the prompt scenario, the object falls vertically without any external horizontal forces. Before the body breaks, it has no horizontal momentum since it is only influenced by gravity moving vertically.
When the object breaks into two parts, their internal forces might change, but their horizontal momentum remains zero. No new horizontal forces are introduced, meaning the total horizontal momentum before and after the break must be the same鈥攝ero. This confirms that the overall system's center of mass doesn't shift horizontally.
  • Momentum is conserved in absence of external forces.
  • The system's initial horizontal momentum is zero.
  • No horizontal forces mean momentum remains constant at zero.
Horizontal Motion
Horizontal motion refers to any movement parallel to the horizon or any flat surface. In our exercise, the center of mass could only shift horizontally if there were horizontal forces at play. However, since the body falls strictly vertically under gravity, no such forces exist.
By analyzing this system, the breaking of the object introduces internal forces that can alter each piece's velocity. However, these solely affect the vertical plane and leave the horizontal plane unchanged. Consequently, both pieces continue moving based on the original momentum condition鈥攏o horizontal motion.
  • Initially, no horizontal movement or forces are present.
  • Breaking alters internal dynamics but doesn't introduce horizontal forces.
  • Horizontal motion of the center of mass remains nonexistent.
Gravitational Force
Gravity plays a crucial role in determining the motion of objects. It is the attractive force between two masses: here, the Earth and the falling object. Acting exclusively in the vertical direction, gravitational force affects the body's descent but doesn't influence horizontal motion.
Gravitational force accelerates the object towards the Earth's center, which results in no horizontal movement from gravity alone. Thus, even when the body breaks into two uneven pieces, gravity continues to act vertically on both, maintaining their path and preventing any horizontal displacement of the system's center of mass.
  • Gravity acts vertically, not affecting horizontal motion.
  • It accelerates the object uniformly downwards only.
  • No horizontal component exists for gravitational forces in this scenario.

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Most popular questions from this chapter

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