To determine the missing value in the table, we can observe the relationship between Weight (N) and Extension (m). This relationship follows Hooke's Law, where the extension is proportional to the force (weight):

$\text{Extension} \propto \text{Weight}.$

Given data:

1. Between 0.1 N and 0.4 N:

   • From 0.1 N → 0.125 m
   • At 0.4 N → 0.5 m.

   The extension triples (0.125 → 0.5), so the relationship is linear.

2. To find the missing extension for 0.2 N: Since 0.2 N is double 0.1 N, the extension must also double: $0.125 \times 2 = 0.25.$

3. To find the missing extension for 0.8 N: Since 0.8 N is 8 times 0.1 N, the extension must scale similarly: $0.125 \times 8 = 1.0.$

Final table:

Answers:

1. Gap 1 = 0.25
2. Gap 2 = 1.0

Would you like more clarification or a deeper explanation of Hooke's Law?

Related Questions:

1. What is Hooke's Law, and how does it relate to springs?
2. How do you determine proportional relationships in experiments?
3. What are the units for force and extension in spring experiments?
4. How can we calculate the spring constant using Hooke's Law?
5. What would happen if we increased the weight beyond 0.8 N?

Tip:

Linear relationships in tables can be identified by observing constant ratios between values!