Effect of the load sequence on the deformation of a spring

Click For Summary

Homework Help Overview

The discussion revolves around the effect of load sequence on the deformation of a spring, specifically examining how different masses affect the deflection of a spring balance. Participants are exploring the relationship between mass, force, and spring deflection.

Discussion Character

  • Conceptual clarification, Mathematical reasoning, Assumption checking

Approaches and Questions Raised

  • Participants are discussing the proportionality of spring deflection to the force applied, questioning whether the deflection 'l' when mass 'm' is applied alone is less than the deflection 'x-d' observed when both masses are present. There is also a focus on the implications of the spring's definition and the calculations involved in determining forces and deflections.

Discussion Status

The discussion is ongoing, with some participants providing insights into the principles governing spring behavior and raising questions about the implications of these principles. There is an exploration of different interpretations regarding the relationship between deflections and forces, but no consensus has been reached yet.

Contextual Notes

Participants are working under the assumption that the spring is initially at rest and that the forces involved are due to gravitational effects on the masses. The discussion also hints at the need for clarity regarding the definitions and relationships in spring mechanics.

Nayef
Messages
3
Reaction score
0
Thread moved from the technical forums, so no Homework Template is shown
Consider a spring balance with no initial deflection. Let an object of mass 'm' be attached to it. We allow the spring to come into equlibrium, and 'd' is the deflection at this eqb position. We add another object of mass 'M', while m is also present, so that the final position is x, and hence deflection between the two equilibrium stages is x-d. Now, let 'm' be attached on its own from the zero position of spring and let 'l' be the deflection produced. Will 'l' be less than x-d?
 
Physics news on Phys.org
The deflection of a spring is always proportional to the force on the spring, regardless of load sequence. The proportionality constant is the spring rate, normally measured in N/meter or lbs/inch.

At steady state (nothing is moving), the force is due to the mass times gravity. If the mass is dropped onto the spring, an additional force due to the mass times the acceleration is added to the force due to gravity.
 
For the purpose of clarity, does your answer imply that l = x-d?
 
The definition of a spring is Force = Spring Rate X Distance (F = K*x). The distance is the amount of spring compression/tension from its free length. Therefore, if you compress a spring a little bit, you will get a force. Compress it a little farther, and the force will increase. The difference between the two forces is equal to the amount of additional compression times the spring rate. The total force is equal to the the total amount of compression from the free length times the spring rate.

You can calculate two different forces, and subtract. Or you can take the difference between the two compressed lengths and multiply by the spring rate. The force difference will be same either way. You can prove it with some high school algebra.
 

Similar threads

Replies
6
Views
1K
  • · Replies 4 ·
Replies
4
Views
2K
  • · Replies 5 ·
Replies
5
Views
1K
  • · Replies 2 ·
Replies
2
Views
2K
Replies
1
Views
1K
  • · Replies 8 ·
Replies
8
Views
2K
  • · Replies 13 ·
Replies
13
Views
1K
  • · Replies 7 ·
Replies
7
Views
1K
Replies
7
Views
1K
  • · Replies 5 ·
Replies
5
Views
2K