Center of mass and Newton's laws of motion

AI Thread Summary
The discussion centers on calculating the speed of the center of mass for a system of two particles, one weighing 2 kg and the other 3 kg, with a 6 N force applied to the 3 kg particle. The initial calculations incorrectly assumed the speed of the 3 kg particle as the speed of the center of mass, leading to confusion. It is clarified that the center of mass speed must consider both particles, with the stationary 2 kg particle affecting the overall motion. The momentum of the system can be used to find the center of mass speed, which is determined to be 6 m/s after proper analysis. Understanding the definition and calculation of center of mass is essential for solving such problems accurately.
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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