Answer to Question #186112 in Physics for Mekaylia

Question

 When two springs (with spring constants k1 and k2) are connected in series, or in parallel, the effective spring constant keff is given by one of the following:

𝑘eff= 𝑘1+𝑘2 OR 1𝑘eff= 1/(𝑘1+1𝑘2)

a) Suppose two springs (with spring constants k1 and k2) are connected in parallel. Predict whether keff will be greater than, or less than, k1 and k2. Check by an experiment if your prediction is correct or not. Hence, determine which of the above two equations is valid for parallel combination of springs.

b) Suppose two springs (with spring constants k1 and k2) are connected in series. Predict whether keff will be greater than, or less than, k1 and k2. Check by an experiment if your prediction is correct or not. Hence, determine which of the above two equations is valid for series combination of springs.

Answer 1

a) Two springs connected in parallel will be stiffer and my experiment confirmed this assumption. So, the correct equation for parallel connection is

$$k_\text{eff}=k_1+k_2.$$

b) Two spring connected in series are less stiff than a single spring, and my experiment confirmed it. So, the effective spring constant is

$$k_\text{eff}=\frac{k_1k_2}{k_1+k_2}.$$