https://r2.erweima.ai/mathbot/image/172571764041382djjbfa.jpg

The table shows the extension in length of a spiral spring when various loads are suspended from it. It can be solved using Hooke's Law in physics, which relates the force applied to the extension of a spring.

### Hooke's Law:
\[ F = k \cdot x \]
Where:
- \( F \) is the force applied (weight of the load in newtons),
- \( k \) is the spring constant,
- \( x \) is the extension (in cm).

The weight \( F \) is calculated from the load using the formula:
\[ F = m \cdot g \]
Where:
- \( m \) is the mass (in grams, converted to kilograms by dividing by 1000),
- \( g \) is the acceleration due to gravity (approximately \( 9.8 \, \text{m/s}^2 \)).

Given this, the problem can be simplified by finding the spring constant \( k \) from the data and applying it to other situations. Here's how to approach the solution:

1. **Convert the Load to Newtons (N)** by multiplying the mass (in kg) by the gravitational constant \( g \).
2. **Find the Spring Constant \( k \)** by selecting any point in the data (preferably using linear regions of the table).
3. **Use \( k \) to check other extensions** by rearranging Hooke's Law \( k = \frac{F}{x} \).

### Example:

For a load of \( 50 \, \text{gm} \), we have:
- \( F = 50 \times 9.8 / 1000 = 0.49 \, \text{N} \).
- The extension \( x = 10.7 \, \text{cm} \).

The spring constant \( k \) is:
\[ k = \frac{0.49}{10.7} \, \text{N/cm} \approx 0.04579 \, \text{N/cm}. \]

Using this spring constant, you can predict extensions for other loads and compare them to the values provided in the table.

Would you like to see the calculations for other points or need further details?

### Related Questions:
1. What happens if we double the load on the spring?
2. How does changing the spring constant affect the extension?
3. Can Hooke's Law apply to all types of springs or only specific ones?
4. What are the units of the spring constant, and why are they important?
5. How would the experiment change if we use a spring with a different material?

### Tip:
When dealing with springs, always remember that Hooke's Law is only valid up to the elastic limit of the spring!

Solve this using Hooke's Law and the data in the table.

Learn how to calculate the extension of a spiral spring when different loads are applied using Hooke's Law. The table shows the relationship between load and extension, and this solution includes key physics concepts like spring constants and force-extension relationships.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation