# Two springs can be combined in series or in parallel. Find the force constant of each combination.

SEE ATTACHMENT #1 for a diagram of the springs and both arrangements.

Spring A has force constant kA= 60 nt/m. Spring B has force constant kB= 40 nt/m.

The two springs attached end to end form a series combination with force constant Ks.

The two springs attached side by side so that a force applied to the ends stretches both springs, form a parallel combination with force constant Kp.

PART a. Find Ks, the force constant of the series combination.

PART b. Find Kp, the force constant of the parallel combination.

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#### Solution Preview

The general relationship between applied force and deformation of a perfectly elastic object such as a spring is:

(1) F = k x, in which F is the force applied to stretch or compress the spring, x is the amount of stretch or compression, and k is its 'force constant'.

PART a.

Step 1.

A solution best begins with a careful diagram of the event. Fig. 1 in ATTACHMENT #1 shows that since the force constants are different, the springs' stretch ...

#### Solution Summary

The force constant of the series and parallel combinations are examined. In a step by step solution, the problem is explained and solved.