- #1

GoGoGadget

- 31

- 0

## Homework Statement

Draw a picture of a spring connected over pulleys to two hanging objects of equal

weight at equilibrium. Determine the relationship of forces among each individual object, then find a final equation that describes the overall relationship of the objects to one another.

## Homework Equations

F = ma

Hooke's law for springs:

F

_{s}= -kx

## The Attempt at a Solution

Body-diagram of the model described above is attached to this post. I know the equation for describing the force of a spring is by Hooke's Law:

F

_{s}= -kx

Forces acting on just the spring (for both directions):

F

_{y}= ma

_{y}= 0

F

_{x}= T-kx = ma

_{x}

Forces acting on M1 & M2:

F

_{x}= ma

_{x}= 0

F

_{y}= T-mg = ma

_{y}= 0

T-mg = 0

T = mg

Relationship of spring with M1 & M2:

So if T = mg, we can substitute T for mg in the equation. I know we need to subtitute the equation so the relationship can be determined on one component and for this, I did it for the x axis. Here's what I have so far:

F

_{x}= ma

_{x}

-kx-M1-M2=ma

_{x}

From here, I'm not sure what to do. On the one hand, I know that the masses on both ends of the spring on going to keep extending the spring out. And I know that the masses are going to be proportional to one another as the spring continues to extend. However, I'm not sure what to make of the ma

_{x}portion of the equation. I know that M1 and M2 are equivalent to the force of mg but when the m in the mz

_{x}is divided, that would cancel out the "m" variables of M1 and M2. Any help from here is appreciated.