Multiple-spring system problem....

[Mike Howard]

The product I'm working on designing simplifies down to a relatively simple three-spring system, which is easily calculated. Unfortunately our company president is weighing in on the design, and doesn't agree with the calculation, and insists the result is something different (based on a fundamentally wrong assumption). I've outlined the problem with a diagram in the attached PDF. At the bottom there are the two different assumptions which were used to come up with the two different results, any assistance into which theory is correct would be greatly appreciated.

Thanks.

 

[tech99]

The product I'm working on designing simplifies down to a relatively simple three-spring system, which is easily calculated. Unfortunately our company president is weighing in on the design, and doesn't agree with the calculation, and insists the result is something different (based on a fundamentally wrong assumption). I've outlined the problem with a diagram in the attached PDF. At the bottom there are the two different assumptions which were used to come up with the two different results, any assistance into which theory is correct would be greatly appreciated.

Thanks.

If the system is in static equilibrium, then the forces on the left hand moveable member must be equal and opposite, F1=F2. And similarly for the right hand moveable member, F3=F2. The forces on the fixed member are also equal and opposite, because F1=F3.

 

[Mike Howard]

If the system is in static equilibrium, then the forces on the left hand moveable member must be equal and opposite, F1=F2. And similarly for the right hand moveable member, F3=F2. The forces on the fixed member are also equal and opposite, because F1=F3.

Thanks. So based on that the total tension in the extension spring (which is the big debate) is 2x F1, as its being acted on and extended at both ends, correct?

 

[tech99]

Thanks. So based on that the total tension in the extension spring (which is the big debate) is 2x F1, as its being acted on and extended at both ends, correct?

The extension spring applies force F2 to each of the moveable members. But the tension in the spring is just F2. Imagine a weight hanging up by a rope. If the tension in the rope is 1N, it applies 1N to the weight and 1N to the support.