Question

A stick of mass 6 kg lies on a smooth sheet of ice. A stone of mass 1.2 kg sliding along the ice at $8 \mathrm{~m} / \mathrm{sec}$ hits the stick perpendicularly at some point and rebounds at $2 \mathrm{~m} / \mathrm{sec}$. Describe the subsequent motion of the center of mass of the stick.

Name: Problem 42, Chapter 7: Elements of Physics for Students of Science and Engineering
Uploaded: 2021-12-19T15:37:11-08:00
Duration: 1 min 9 s
Channel: Manish Jain
Description: A stick of mass 6 kg lies on a smooth sheet of ice. A stone of mass 1.2 kg sliding along the ice at 8 m / sec hits the stick perpendicularly at some point and rebounds at 2 m / sec. Describe the subsequent motion of the center of mass of the stick.

   A stick of mass 6 kg lies on a smooth sheet of ice. A stone of mass 1.2 kg sliding along the ice at $8 \mathrm{~m} / \mathrm{sec}$ hits the stick perpendicularly at some point and rebounds at $2 \mathrm{~m} / \mathrm{sec}$. Describe the subsequent motion of the center of mass of the stick.

Elements of Physics for Students of Science and Engineering

George Hiram… 2nd Edition

Chapter 7, Problem 42

Instant Answer

Solved by Expert Manish Jain

12/19/2021

Step 1

2$ kg - Initial velocity of stone: $v_{p1} = 8$ m/s - Final velocity of stone after collision: $v_{p2} = 2$ m/s (in the opposite direction) - The stick is initially at rest on a smooth (frictionless) ice surface - The stone hits the stick perpendicularly Show more…

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A stick of mass 6 kg lies on a smooth sheet of ice. A stone of mass 1.2 kg sliding along the ice at $8 \mathrm{~m} / \mathrm{sec}$ hits the stick perpendicularly at some point and rebounds at $2 \mathrm{~m} / \mathrm{sec}$. Describe the subsequent motion of the center of mass of the stick.

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Key Concepts

Conservation of Linear Momentum

In an isolated system with negligible external forces, the total linear momentum remains constant across any collision. This principle allows us to equate the momentum before and after an impact, thereby enabling the calculation of the resulting motion of the system's components.

Motion of the Center of Mass

The center of mass of a system serves as the effective point where the system's mass can be considered to be concentrated. In the absence of external forces, the center of mass moves with constant velocity, determined by the total momentum and mass of the system. This concept is crucial in analyzing systems after collisions, as it remains unaffected by internal forces.

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