Center of mass and Newton's laws of motion

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Homework Help Overview

The discussion revolves around a problem involving two particles with masses of 2 kg and 3 kg, initially at rest, with a 6 N force applied to the 3 kg particle. Participants are exploring how to determine the speed of the center of mass after 5 seconds.

Discussion Character

  • Exploratory, Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • Participants discuss the application of Newton's laws and the calculation of acceleration and velocity for the 3 kg particle. Questions arise about the initial velocity of the center of mass and the implications of applying force to an unconnected system. There are inquiries about the definition of center of mass and its calculation.

Discussion Status

The discussion is active, with participants questioning assumptions about the system and exploring different interpretations of the problem. Some guidance has been offered regarding the relationship between momentum and the center of mass, but no consensus has been reached on the specific calculations or definitions needed.

Contextual Notes

Participants are navigating the definitions and equations related to center of mass, with some expressing uncertainty about the foundational concepts necessary to solve the problem. There are also references to external resources for definitions, indicating a lack of clarity on the topic.

Avaron Cooper
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Homework Statement


two particles of 2 kg and 3 kg are at rest .
a 6 N force is exerted on the 3 kg particle at t=0.
what is the speed of the center of mass at t=5s?

Homework Equations


F=ma
v=u+at

The Attempt at a Solution


first i applied f=ma to the 3 kg object and got 2 as the accn. And applied v= u+ at and got10 as the velocity but the answer is 6. Can someone show me where I went wrong please?
 
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Avaron Cooper said:

Homework Statement


two particles of 2 kg and 3 kg are at rest .
a 6 N force is exerted on the 3 kg particle at t=0.
what is the speed of the center of mass at t=5s?

Homework Equations


F=ma
v=u+at

The Attempt at a Solution


first i applied f=ma to the 3 kg object and got 2 as the accn. And applied v= u+ at and got10 as the velocity but the answer is 6. Can someone show me where I went wrong please?
What is u?
What is the velocity of the common centre of mass of two particles?
 
U is initial velocity and is zero. Therefore I took the initial velocity of the center of mass as zero.
 
Can we consider the 6N force is applied to both the particles when considering them as one system eventhough they are not connected?
 
Avaron Cooper said:
Can we consider the 6N force is applied to both the particles when considering them as one system eventhough they are not connected?

If you have two footballs (not connected) and you kick one, do they both move?

Regarding the original question, is here a diagram to show the configuration of the masses and the applied force?
 
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⭕2kg ⭕➡6N.
. 3kg
 
One particle is 2 kg while the other is 3 kg and 6 N is applied on 3 kg one only.
 
Avaron Cooper said:
⭕2kg ⭕➡6N.
. 3kg

So, you calculated the speed of the 3kg object after 5 seconds and got 10 m/s. That's clearly not the speed of the centre of mass. So, let's think this through.

IF both masses were moving in the same direction at 10 m/s, THEN the speed of the centre of mass would be 10m/s. But, the first mass isn't moving. So, how could you analyse the motion of the centre of mass in this case?
 
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Avaron Cooper said:
One particle is 2 kg while the other is 3 kg and 6 N is applied on 3 kg one only.
What is your understanding of the definition of "center of mass?" Can you provide a general equation for the location of the center of mass of a system of particles?

Chet
 
  • #10
I can't come up with one... Can you please help me with that sir?
 
  • #11
Avaron Cooper said:
I can't come up with one... Can you please help me with that sir?
It's appropriate to search for that sort of thing on the web rather than ask on a forum. That said, some of the definitions I see out there are not very good. This one is ok: https://en.m.wikipedia.org/wiki/Center_of_mass
 
  • #12
Avaron Cooper said:
I can't come up with one... Can you please help me with that sir?
How did you think you were going to solve a problem involving center of mass if you don't even know it's definition?
 
  • #13
I
Chestermiller said:
How did you think you were going to solve a problem involving center of mass if you don't even know it's definition?
I know what the center of mass is but I don't know any equation to find the center of mass. If I am going to find the center of mass I would take the torques and find it.
 
  • #14
Can I equal the momentum of the moving object to the momentum of the whole system?
 
  • #15
Avaron Cooper said:
Can I equal the momentum of the moving object to the momentum of the whole system?
Momentum is additive. The momentum of the whole system is equal to the sum of the momenta of its component parts. So yes, if there are two pieces and one is stationary (zero momentum) then the momentum of the combined system is equal to the momentum of the other piece alone.

[In classical mechanics], the momentum of the combined system is equal to its total mass multiplied by the velocity of its center of mass. So yes, you could use this line of reasoning to solve the problem.
 
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  • #16
Thank you very much jbriggs444!
 

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