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

In summary, the conversation discusses the problem of finding the center of mass for a solid sphere that has been cut and part of it removed. The solution involves using the center of mass equation and slicing the sphere into discs to integrate over the z-axis. The given hint suggests using symmetry to simplify the calculation process.
  • #1
mlee
24
0
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
 
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  • #2
Welcome to PF!
How are you used to calculating the center of mass of systems consisting of several objects?
 
  • #3
Use the center of mass equation. (((x)1*m(1)) + (x(2)*m(2)) + (x(3)*m(3))) / (m(1) + m(2) + m(3))
 
  • #4
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
 
  • #5
Use that hint!
 

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

The center of mass is the point at which the mass of an object is evenly distributed. In the case of a sphere, the center of mass is located at the exact center of the sphere. However, if a part of the sphere is removed, the center of mass will shift accordingly.

2. Does the size of the remaining part of the sphere affect the center of mass?

Yes, the size of the remaining part of the sphere does affect the center of mass. The larger the remaining part, the closer the center of mass will be to the original center of the sphere. Conversely, if a small part of the sphere is removed, the center of mass will shift further away from the original center.

3. How is the center of mass calculated for a sphere with a remaining part?

The center of mass for a sphere with a remaining part can be calculated using the following formula:
x = (M1x1 + M2x2) / (M1 + M2)
y = (M1y1 + M2y2) / (M1 + M2)
z = (M1z1 + M2z2) / (M1 + M2)
where M1 and M2 are the masses of the two parts, and (x1, y1, z1) and (x2, y2, z2) are the coordinates of their respective centers of mass.

4. Can the center of mass of the remaining part of a sphere be outside of the original sphere?

Yes, it is possible for the center of mass of the remaining part of a sphere to be outside of the original sphere. This can happen if the removed part is significantly larger or heavier than the remaining part, causing the center of mass to shift further away from the original center.

5. How does the shape of the remaining part affect the center of mass?

The shape of the remaining part can also affect the center of mass. For example, if a small slice is removed from the sphere, the center of mass will shift towards the side where the slice was removed. This is because the mass is distributed differently on either side of the removed slice, causing an imbalance in the center of mass.

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