# Resultant Force Acting On Springs : Confused

1. Sep 16, 2010

### cyt91

1. The problem statement, all variables and given/known data
Suppose we have 2 insulated metal rods each measuring 40 cm. Now,the 2 metal rods are connected with 3 identical springs each of length 20 cm (force constant 2.0 N/m) in parallel. A current of 20A is passed through each metal rod in opposing directions. What is the extension of each spring? The springs are initially not stretched.

2. Relevant equations
F=BIL

B= {$$\mu$$ x I}/{2$$\pi$$r}

3. The attempt at a solution
I calculated the force acting on each metal rod to be 0.0036 N. The 2 metal rods repel each other since the current flowing through them is in opposite directions.

Now, my question is what is the resultant force acting on each spring? Is it 0.0012N or 0.0012 x 2 = 0.0024 N since there are 2 forces acting on each spring ; pulling each spring from the 2 ends ?

2. Sep 16, 2010

### zhermes

see this similar post: https://www.physicsforums.com/archive/index.php/t-85739.html

It will actually just be 1xForce, look at it from the perspective of one of the rods. The rod is being pushed away by F newtons, so, for equilibrium the spring must be pulling back with -F newtons, and that -F comes from the extension of the spring.... so the spring must be only extended by F, not 2xF. Thats pretty confusing, but does it make sense?

3. Sep 17, 2010

### cyt91

Actually it makes a lot of sense. Thanks for pointing this out to me.