Concept explainers
The center of mass of the particles which are positioned at the corners of a square with length of sides measuring
Answer to Problem 30P
Position of center of mass
Explanation of Solution
Given info:
Mass of particle A
Mass of particle B
Mass of particle C
Mass of particle D
Length of side of square
Formula used:
The x and y coordinates, of the center of mass of particles of a system in a two dimensional plane is calculated by the following formula:
Wherein
Similarly the y coordinates are given by the following formula:
Wherein
The position of center of mass of a particle having x and y coordinate is given by the formula:
Wherein r is the position of center of mass of the particle, while
Calculation:
As per figure 5-19, the x and y coordinates of position of mass at A is
Similarly the x and y coordinates for the position of mass at B, C and D respectively are
Substituting the various values of masses of particles at points A, B, C and D and also its horizontal distances from origin in the equation:
Similarly substituting the various values of masses of particles at points A, B, C and D and also its vertical distances from origin in the equation:
The position of center of mass is given by the formula:
Substituting
Conclusion:
The x and y coordinates of the particles are
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Chapter 5 Solutions
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- University Physics Volume 1PhysicsISBN:9781938168277Author:William Moebs, Samuel J. Ling, Jeff SannyPublisher:OpenStax - Rice University