Re: why is force shared between springs connected in parallel?

The question: "Why is force shared between springs connected in parallel? If I connected four springs (each with spring constant k = 10) and then applied a force of say 40 newtons, why will each spring experience a force of 10 newtons? (according to my teacher). If springs and capacitors are analogous and so if from f= kx and v = (1/c)Q, the force applied is analogous to voltage in a circuit, why then is the force applied to the springs not the same at each parallel branch if voltages are same across each branch in a parallel circuit? Please help! Thankyou!"

If all four springs are simultaneously supporting, for instance, a box of 40 N weight, each spring will provide 10 N force, assuming the box is evenly distributed over the springs. The total force from the springs must be 40 N or else the net force on the box would not be zero, in which case the box would move! Since the net force is the (vector) sum of all the forces operating on the box, the spring force must be shared by all the springs.

In the analogy of the capacitors it is current that is evenly distributed across a parallel connection! You have to be careful in making analogies, because what is a parallel situation in one analog might be a series situation in another analog. There is a really good web page at swarthmore.edu which does an extremely good job of describing several analogies, including your analogy of springs and capacitors! The differences can be noted primarily by the following table that is given at the swarthmore.edu site:

Notice that in the case of capacitors it is current, not voltage, which sums to zero at nodes.

John Link, MadSci Physicist