The figure below shows two springs connected in parallel. This combination can be thought of as being equivalent to a single spring having an effective force constant keff. Obviously, the effective force constant must be related to the force constants k1 and k2 of the individual springs. We will assume that the springs have no significant mass. Suppose we stretch the combination a total distance x from its equilibrium position.(Figure 1)



If you connect a spring of force constant 35.0N/cm in parallel with one of force constant 55.0N/cm , what is the force constant of the single spring that will be equivalent to this combination?

K = k1 + k2 = 35 + 55 = 90N/cm.

To find the effective force constant, keff, of the parallel combination of two springs with force constants k1 and k2, we can use the formula:

1/keff = 1/k1 + 1/k2

In this case, k1 is the force constant of the first spring, which is 35.0 N/cm, and k2 is the force constant of the second spring, which is 55.0 N/cm.

Substituting the values into the formula, we have:

1/keff = 1/35.0 + 1/55.0

Now, we can simplify this equation to find the value of 1/keff:

1/keff = (55.0 + 35.0)/(35.0 * 55.0)

1/keff = 90.0/1925.0

To find keff, we can take the reciprocal of both sides of the equation:

keff = 1925.0/90.0

keff = 21.39 N/cm

Therefore, the force constant of the single spring that will be equivalent to the combination is approximately 21.39 N/cm.