# Two masses attached to a fixed vertical spring

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1. Jun 10, 2015

### JayB

1. The problem statement, all variables and given/known data
Two mass-less springs with spring constant k = 1000 N/m each have 1 block attached (Spring A is fixed to the ceiling and is attached to a 5 kg Mass A, Spring B is attached and below the 5 kg Mass A and is attached to another 5 kg Mass B at the other end; this system is vertical).
When the masses and springs are resting freely, how far from equilibrium is Spring A extended?

2. Relevant equations
Hooke's Law: Fspring=(k)(-Δd)
Force of gravity: F=mg

3. The attempt at a solution
Finding the solution is straightforward: you ignore Spring B, make the force of gravity on both masses equal to the force exerted by the spring on both masses, and solve for Δd.

I'm having trouble understanding the solution conceptually. I don't understand why Spring B doesn't contribute to the question. Spring B is attached to Mass B so doesn't it help Spring A resist the pull of gravity on the two masses? I thought that the amount of displacement from equilibrium of Spring A would be less with the inclusion of Spring B than without Spring B.

However, according to the solution, having both Mass A and B attached directly to Spring A would yield the same amount of displacement from equilibrium of Spring A as having Spring B in between Spring A and Mass B. I don't understand why and would greatly appreciate if something could clear this up!

2. Jun 10, 2015

### paisiello2

Technically Spring B does contribute since it transmits the force from Mass B to Mass A, doesn't it?

If you think about it, what is Mass A composed of but tiny atoms joined together by atomic forces that are essentially linear springs? But these numerous tiny springs don't enter into the solution either (other than transmitting their individual tiny forces from their masses).

3. Jun 10, 2015

### JayB

Yes you're right that Spring B transmits the force from Mass B to Mass A and in that sense contributes. I meant "contribute" as in "helping" Spring A to resist the pull of gravity.

And thank you for that explanation. I didn't think of it that way: of matter being composed of numerous springs, which we ignore in such questions.

Thank you!