A Level Physics Practice Exam

What is the effect on the spring constant when two springs are arranged in series?

1. The spring constant is doubled

2. The spring constant is halved

3. The spring constant remains the same

4. The spring constant is negligible

The correct answer is: The spring constant is halved

When two springs are arranged in series, the overall spring constant of the system can be understood through the concept of effective stiffness. In a series arrangement, the total spring constant (k_total) can be determined by the formula: \[ \frac{1}{k_{\text{total}}} = \frac{1}{k_1} + \frac{1}{k_2} \] This equation indicates that the reciprocal of the total spring constant is equal to the sum of the reciprocals of the spring constants of each individual spring. As you combine two springs, the overall stiffness decreases because the springs must stretch more to achieve the same force compared to a single spring. If both springs are identical and each has a spring constant k, the effective spring constant would be: \[ \frac{1}{k_{\text{total}}} = \frac{1}{k} + \frac{1}{k} = \frac{2}{k} \] From this, it follows that: \[ k_{\text{total}} = \frac{k}{2} \] This result shows that the effective spring constant of two springs in series is indeed half of the spring constant of a single spring. Therefore, the correct conclusion is