What would happen if a spring was between two moving objects?

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Discussion Overview

The discussion explores the dynamics of a spring placed between two moving objects of different masses. Participants consider how the spring interacts with the objects, particularly in terms of force distribution, acceleration, and work done on each object. The scope includes conceptual reasoning and technical explanations related to mechanics.

Discussion Character

  • Exploratory
  • Technical explanation
  • Conceptual clarification

Main Points Raised

  • One participant questions how a spring would behave if placed between a stationary wall and a moving object, specifically regarding force distribution when both ends are attached to objects of different masses.
  • Another participant suggests that the spring would push both objects with the same force, regardless of their motion or mass.
  • There is uncertainty about which object would receive more work from the spring, with one participant hypothesizing that the heavier mass would receive more work due to slower acceleration.
  • A later reply clarifies that the spring applies equal and opposite forces to both masses and that both masses leave the spring when it reaches its unstretched length, challenging the initial assumptions about work distribution.
  • It is noted that the center of mass of the system does not move, and the lighter mass ultimately receives more kinetic energy.

Areas of Agreement / Disagreement

Participants express differing views on the distribution of work and the behavior of the spring, indicating that the discussion remains unresolved regarding the specifics of how force and work are distributed between the two masses.

Contextual Notes

Some assumptions about the initial conditions of the masses are not explicitly stated, such as whether they are at rest before the spring is engaged. The discussion also does not resolve how the spring's behavior might change if the objects were in motion prior to engagement.

lluke9
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Hey people!

So, what would happen? (This is not a school question, I was just wondering!)

Say, a spring is between a totally unmoving wall and a 1 kg object. The spring pushes on the object with 1 Newton of force. The block accelerates at 1 m/s^2.

But... what if the wall WASN'T unmoving... what it it were ANOTHER object with a mass of 2 kg?
Would the spring somehow split the force 2/3 to 1/3? Or split the force evenly among the two blocks, making one accelerate at .5 m/s^2 and the other at .25 m/s^2?
What will it do!?
Can someone explain what would happen and why? I think I can imagine what would happen, but I'm not sure why.

Thanks and hi!
 
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Welcome to PF!

When a spring pushes on two objects, there is essentially one force, pushing in two different directions. It doesn't matter if the objects are stationary or moving.
 
So even if the two objects had different masses, the spring would push both with the same force?
Hmm...

Then, will the spring push for a longer time on the object with less mass or more mass?
In other words, which block receives more work?
I'm THINKING it's the one with more mass, because it will accelerate slower and stay on the spring longer.
But when the lighter mass leaves the spring, won't the spring just pop into equilibrium without something to push off of? So that means the one with less mass actually receives more work...

Sorry, but can I get some more help here?
 
The spring pushes on both masses for the same amount of time, with equal and opposite forces at each end. It doesn't "pop" into equlibrium. Both masses will leave the spring when it reaches its unstretched length and stops applying any force.

You seem to be assuming both masses are initially at rest, though you don't actually say that. Because all the forces within the system are equal and opposite, the center of mass of the complete system never moves.

So if the masses are m_1 and m_2, their final velocities will be -p/m_1 and p/m_2 where p is the momentum of one mass, and the kinetic energies will by p^2/(2m_1) and p^2/(2m_2). So you are right, the lighter mass gets more kinetic energy.
 

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