A force of 10N extends a spring of natural length 1m by 0.02m, calculate the length of the spring when the applied force is 40N.

Analysis

To solve this problem, we use Hooke’s Law, which states that the force applied to a spring is directly proportional to its extension, provided the elastic limit is not exceeded.

Concept

The formula for Hooke's Law is:

Where:

• $F$ = Applied force (in Newtons)
• $k$ = Spring constant (in N/m)
• $e$ = Extension (in meters)

The extension ($e$) is the difference between the new length ($L$) and the natural length ($L_0$):

Step-by-Step Solution

Step 1: Find the spring constant ($k$) using the first set of data. Given: $F_1 = 10\text{N}$, $e_1 = 0.02\text{m}$

Step 2: Calculate the extension ($e_2$) for the new force ($F_2 = 40\text{N}$). Using the same spring constant ($k = 500\text{ N/m}$):

Step 3: Calculate the total length of the spring. The total length ($L_2$) is the sum of the natural length ($L_0$) and the new extension ($e_2$):

Conclusion

The total length of the spring when a force of 40N is applied is 1.08m.

Exam Tip

Always distinguish between extension and total length. Many students calculate the extension (0.08m) and stop there, forgetting to add it back to the original natural length (1m). Always re-read the question to see if it asks for the extension or the final length!