Center of Mass Blocks Problem

In summary: So if there are 10 blocks with masses of 1 kg each, and 5 blocks with masses of 2 kg each, the center of mass would be at (2 * 2)/(10) = 2.5 kg. centers of mass are important in physics because they help determine where objects will go and how fast.
  • #1
sweatband
16
0

Homework Statement



Consider a system of two blocks that have masses m_1 and m_2. Assume that the blocks are point-like particles and are located along the x-axis at the coordinates x_1 and x_2. In this problem, the blocks can only move along the x axis. Find the x coordinate of the center of mass of the system.

Homework Equations



The solution is ( [tex]\((m1x1 + m2x2)/(m1 + m2)[/tex], but I cannot for the life of me understand why this is exactly. Why multiply the mass by the x-coordinate of its location?

The Attempt at a Solution

 
Last edited:
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  • #2
What is the general formula / definition of center of mass ?
 
  • #3
Are you questioning the definition of center of mass? Maybe this brief discussion will help: Center of Mass
 
  • #4
Center of mass: The point that represents the "average" position of the entire mass of a system.
 
  • #5
sweatband said:
Center of mass: The point that represents the "average" position of the entire mass of a system.

well hmm yes and no, i meant: formulate it with an expression.
See the link that Doc Al posted.
 
  • #6
What I don't understand is the algebra of arriving at that equation, and thanks for that link, Doc Al, I'm looking over it now
 
  • #7
sweatband said:
What I don't understand is the algebra of arriving at that equation, and thanks for that link, Doc Al, I'm looking over it now


Well the thing is that the definition is purley mathametical, and trying to explain it in words are just secondary. The definition of center of mass is the formulas that is posted on that link.
 
  • #8
Awsome, the link answers my all my questions, thanks guys!
 
  • #9
sweatband said:
Awsome, the link answers my all my questions, thanks guys!

great that we could help you. But don't you own a book for the course? This is standard mechancs #1 :P
 
  • #10
sweatband said:
Center of mass: The point that represents the "average" position of the entire mass of a system.
You can think of it (loosely) as the weighted average position of the mass in a system. Not just the average. A part of the system with twice the mass (as some other part) gets counted twice (compared to that other part).
 

1. What is the center of mass for a block?

The center of mass for a block is the point at which an object's mass is evenly distributed in all directions. It is the point at which the object can be balanced on a pivot without tipping over.

2. How is the center of mass calculated for a block?

The center of mass for a block can be calculated by adding up the individual masses of all the parts of the block and dividing that by the total mass. It can also be calculated by finding the average of the individual x and y coordinates for each particle in the block.

3. What factors affect the center of mass for a block?

The center of mass for a block can be affected by its shape, size, and distribution of mass. For example, a block with a larger mass on one side will have a center of mass closer to that side.

4. Why is the center of mass important to understand?

The center of mass is important to understand because it helps us predict how an object will behave when acted upon by external forces. It also plays a role in determining an object's stability and ability to balance.

5. How does the center of mass affect the motion of a block?

The center of mass affects the motion of a block by determining its overall movement and rotation. If the center of mass is located off-center, the block will experience a torque and rotate until the center of mass is directly above the supporting base. This also affects the block's stability and ability to maintain its position.

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