2 Masses connected by a spring

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To find the acceleration of a system with two masses connected by a spring, it's essential to draw free body diagrams for each mass and account for all forces, including the spring's force. The acceleration of the larger mass, calculated as 5 m/s², may be incorrect if the spring's restoring force is not considered. The downward forces are irrelevant in a frictionless horizontal setup, where only horizontal forces affect acceleration. The proper approach involves including the spring's force in the calculations rather than simply adding the accelerations of each mass. Understanding the dynamics of coupled masses is crucial for accurate results in such systems.
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Hello I am trying to find the acceleration of a system that has 2 masses, m1 and m2 connected via a spring with a spring constant of k with a force of F applied to the larger mass in the direction that stretches the spring.
 
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Very good. How are you going about it?
ie. did you try Newton's method of drawing free body diagrams for each mass?
 
Simon Bridge said:
Very good. How are you going about it?
ie. did you try Newton's method of drawing free body diagrams for each mass?

Yeah I found the forces acting downwards but I think they are irrelevant because all the acceleration for the system would be in the sideways direction. I found that the acceleration of the 3kg (larger) mass is 15/3= 5ms/^2, but I'm not sure if this is correct because wouldn't the spring be pulling back on it and therefore lowering its acceleration? I am not really sure how to find the acceleration of the whole system, do I try find the acceleration of each mass and add them? How do I do that when a spring is involved?
 
glover261 said:
Yeah I found the forces acting downwards but I think they are irrelevant because all the acceleration for the system would be in the sideways direction.
I think you may have left out some important information in your problem statement:
I was imagining both masses on a level frictionless surface with one to the left of the other ... in that situation the sum of the vertical (acting downwards) forces is zero.

I found that the acceleration of the 3kg (larger) mass is 15/3= 5ms/^2,...
This cannot follow from post #1 because you have not given any values for m1, m2 or F. It is unlikely to be correct because you have not accounted for the force from the spring.

...but I'm not sure if this is correct because wouldn't the spring be pulling back on it and therefore lowering its acceleration?
Yes.

I am not really sure how to find the acceleration of the whole system, do I try find the acceleration of each mass and add them?
This is not how you would normally treat the accelerations of coupled masses is it?

How do I do that when a spring is involved?
You include the force due to the spring in the free body diagram.
Think how you would do this problem if the spring were replaced by a string?
 

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