Why Measure the Center of Mass from the Same Position After a Collision?

In summary, the center of mass must be measured from the same position after the collision in order to find the change in COM.
  • #1
String theory guy
26
4
Homework Statement
Why must you measure the COM of a system from the origin before and after a collision?
Relevant Equations
COM formula
For example, in the problem below, if the center of mass is chosen to be measured initially at the center of the left mass, then it must be measured from the same position after the collision.

EIDLa.png


This gives an initial COM of,

LO37h.png


and finial COM of,

8Kltp.png


Which gives their change in center of mass of the system.

So why must I find the finial COM of the system with respect to the same place which I used to find the COM before the force was exerted on the system.
 
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  • #2
String theory guy said:
Homework Statement:: Why must you measure the COM of a system from the origin before and after a collision?
Relevant Equations:: COM formula

For example, in the problem below, if the center of mass is chosen to be measured initially at the center of the left mass, then it must be measured from the same position after the collision.

View attachment 318103

This gives an initial COM of,

View attachment 318104

and finial COM of,

View attachment 318105

Which gives their change in center of mass of the system.

So why must I find the finial COM of the system with respect to the same place which I used to find the COM before the force was exerted on the system.
Because what we are trying to find is how far the CoM moved.
 
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  • #3
String theory guy said:
Homework Statement:: Why must you measure the COM of a system from the origin before and after a collision?
Relevant Equations:: COM formula

For example, in the problem below, if the center of mass is chosen to be measured initially at the center of the left mass, then it must be measured from the same position after the collision.

View attachment 318103

This gives an initial COM of,

View attachment 318104

and finial COM of,

View attachment 318105

Which gives their change in center of mass of the system.

So why must I find the finial COM of the system with respect to the same place which I used to find the COM before the force was exerted on the system.
You can measure the center of mass from any position as long as you do it from the same place before any after the force. Hope that helps.
 
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1. Why is it important to measure the center of mass from the same position after a collision?

Measuring the center of mass from the same position after a collision allows for accurate calculations of the momentum and energy involved in the collision. This information is crucial in understanding the dynamics of the collision and determining the cause of the collision.

2. How is the center of mass measured after a collision?

The center of mass can be measured using various techniques such as video analysis, motion sensors, or manually measuring the position of objects involved in the collision. The key is to measure the position of the center of mass of the system before and after the collision from the same reference point.

3. What is the significance of measuring the center of mass from the same position in a collision?

By measuring the center of mass from the same position, we can accurately determine the change in the momentum and energy of the system during the collision. This information is crucial in understanding the laws of motion and the conservation of momentum and energy.

4. Can the center of mass be measured from any point after a collision?

No, the center of mass must be measured from the same reference point before and after the collision to ensure accuracy. If measured from different points, the results may not reflect the true change in momentum and energy of the system.

5. Why is the center of mass considered to be a fixed point in a collision?

The center of mass is considered a fixed point because it remains constant throughout the collision, regardless of the external forces acting on the system. This allows for the accurate measurement of the change in momentum and energy of the system.

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