What is the center of mass of the remaining part of the sphere ?

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Discussion Overview

The discussion revolves around calculating the center of mass of a solid sphere after a portion above a certain height has been removed. The problem is presented in a mathematical context, focusing on the application of integration and symmetry in determining the center of mass of the remaining part of the sphere.

Discussion Character

  • Homework-related
  • Mathematical reasoning

Main Points Raised

  • One participant expresses confusion about how to solve for the center of mass after a portion of the sphere is removed.
  • Another participant asks about the methods used to calculate the center of mass for systems with multiple objects.
  • A suggestion is made to use the center of mass equation, providing a formula that incorporates the masses and positions of different parts.
  • It is noted that by symmetry, the center of mass will lie along the z-axis, and a method involving slicing the sphere into discs and integrating over z is proposed.
  • Participants encourage the use of the symmetry hint provided to aid in the calculation.

Areas of Agreement / Disagreement

Participants generally agree on the approach of using symmetry and integration to find the center of mass, but the discussion remains unresolved as no specific calculations or definitive answers have been provided.

Contextual Notes

The discussion does not address specific assumptions about the density distribution of the sphere or the exact method of integration, leaving these aspects open for further clarification.

mlee
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Please who can solve this for me... :frown:
Many thanx

A solid sphere has a mass of 25 kg and a radius of 30cm. The center of the sphere is placed at the origin,x=0,y=0,z=0. The sphere is cut and the part of the sphere above z=7cm is removed.
What is the center of mass of the remaining part of the sphere ?

PLease help me, i am very confused...
Thank you very much
 
Physics news on Phys.org
Welcome to PF!
How are you used to calculating the center of mass of systems consisting of several objects?
 
Use the center of mass equation. (((x)1*m(1)) + (x(2)*m(2)) + (x(3)*m(3))) / (m(1) + m(2) + m(3))
 
there's a given hint: by symmetrie u can see that the center of mass lies along the z-axis. slice the sphere up in discs of thickness dz and integrate over z to find the center of mass
 
Use that hint!
 

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