Two masses attached to a fixed vertical spring

In summary, a system consisting of two mass-less springs with spring constant k = 1000 N/m each and two 5 kg masses (Mass A and Mass B) is described, with Spring A attached to the ceiling and Mass A and Spring B attached to Mass B. The question asks for the displacement from equilibrium of Spring A when the system is at rest. Using Hooke's Law and the force of gravity, the solution is found by considering only the forces on Mass A and setting them equal to the force exerted by Spring A. This means that the contribution of Spring B is ignored in the calculation. This may seem counterintuitive, but it can be understood by thinking of Mass A as composed of tiny linear springs, whose
  • #1
JayB
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Homework Statement


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?

Homework Equations


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

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!
 
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  • #2
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).
 
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  • #3
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!

paisiello2 said:
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).
 

FAQ: Two masses attached to a fixed vertical spring

1. What is the principle behind two masses attached to a fixed vertical spring?

The principle behind two masses attached to a fixed vertical spring is Hooke's law, which states that the force exerted by a spring is directly proportional to the displacement of the spring from its equilibrium position.

2. How are the masses and the spring connected in this system?

The two masses are connected to the spring by being attached to each end of the spring. The spring is fixed vertically, meaning it is attached to a stationary point.

3. How does the mass of each object affect the behavior of the system?

The mass of each object affects the behavior of the system by determining the amplitude and frequency of the resulting oscillations. Heavier masses will result in slower oscillations, while lighter masses will have faster oscillations.

4. What factors can change the frequency of oscillations in this system?

The frequency of oscillations in this system can be changed by altering the masses of the objects, the stiffness of the spring, and the gravitational pull on the objects.

5. How is the energy transferred between the masses and the spring in this system?

The energy is transferred between the masses and the spring in this system through the process of oscillation. As the masses move back and forth, they transfer energy to the spring, which then stores and releases it as potential and kinetic energy.

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