Mechanics - centre of mass lamina

In summary, the conversation is about finding the centre of mass of a lamina, specifically a square with a triangle removed and a particle attached. The solution involves using the coordinates of the centre of mass of each body and applying the concept of negative mass for the triangle.
  • #1
kolomsg
2
0
hi, I'm stuck and I can't seem to find a simple solution to questions regarding how to find the centre of mass of a lamina.

for example:
A uniform lamina with mass/unit area 0.12grams/cm2 consists of a square of
side 80cm, with one corner at the origin O(0, 0) and other corners at B(80, 0),
C(80, 80) and D(0, 80). A triangle of material has been removed from one corner
by cutting a straight line from E(50, 0) to F(80, 40), and a particle of mass 0.5kg
is attached at C. Find the coordinates of the centre of mass.
If anyone could help me, that'd be much appreciated. thanks
 
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  • #2
Welcome to PF!

Hi kolomsg! Welcome to PF! :smile:

Do you know how to find the coordinates of the centre of mass of several bodies, given that you know the coordinates of the centre of mass of each?

Apply that to the square, the triangle, and the particle, but with the triangle having negative mass! :wink:
 
  • #3
hi, thanks a lot. it helped!
 

What is the definition of centre of mass for a lamina?

The centre of mass for a lamina is the point at which the entire mass of the lamina is considered to be concentrated. It is the point at which the lamina can be balanced in any direction without any rotation.

How is the centre of mass for a lamina calculated?

The centre of mass for a lamina is calculated by taking the average of the position of all the individual masses within the lamina, weighted by their respective masses. This can be represented mathematically as:
x̄ = (m1x1 + m2x2 + ... + mnxn) / (m1 + m2 + ... + mn),
where x̄ is the x-coordinate of the centre of mass, m is the mass of each individual point, and x is the x-coordinate of each individual point.

What is the difference between centre of mass and centroid?

The centre of mass and centroid are often used interchangeably, but they have different definitions. The centre of mass is the point at which the entire mass of the lamina is concentrated, while the centroid is the geometric centre of the lamina. In most cases, the centre of mass and centroid are the same point, but they can differ if the lamina has a non-uniform density.

How does the distribution of mass affect the centre of mass for a lamina?

The distribution of mass within a lamina affects the position of the centre of mass. If the mass is evenly distributed, the centre of mass will be at the geometric centre of the lamina. However, if the mass is concentrated towards one side, the centre of mass will be closer to that side. The centre of mass can also be outside of the lamina if there is a void or a hole within the lamina.

Why is the centre of mass important in mechanics?

The centre of mass is important in mechanics because it is the point at which the entire mass of an object can be considered to act. This allows for simplification of calculations and analysis, as the motion of an object can be described by the motion of its centre of mass. It is also important in determining the stability and equilibrium of an object, as any external force acting on the centre of mass will not cause rotation.

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