Center of mass and Newton's laws of motion

[Avaron Cooper]

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?

 

[ehild]

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?

 

[Avaron Cooper]

U is initial velocity and is zero. Therefore I took the initial velocity of the center of mass as zero.

 

[Avaron Cooper]

Can we consider the 6N force is applied to both the particles when considering them as one system eventhough they are not connected?

 

[PeroK]

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?

 

[Avaron Cooper]

2kg ➡6N.
. 3kg

 

[Avaron Cooper]

One particle is 2 kg while the other is 3 kg and 6 N is applied on 3 kg one only.

 

[PeroK]

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?

 

[Chestermiller]

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

 

[Avaron Cooper]

I can't come up with one... Can you please help me with that sir?

 

[haruspex]

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

 

[Chestermiller]

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?

 

[Avaron Cooper]

I

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.

 

[Avaron Cooper]

Can I equal the momentum of the moving object to the momentum of the whole system?

 

[jbriggs444]

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.

 

[Avaron Cooper]

Thank you very much jbriggs444!