D Part (c) Write an equation for the work done in stretching the spring from x1 to x₂. Part (d) Calculate the work done, in joules, in stretching the spring from x1 to x₂. Part (e) Calculate the work, in joules, necessary to stretch the spring from x = 0 to x3.

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### Problem 2

A certain spring has a spring constant \( k_1 = 660 \, \text{N/m} \) as the spring is stretched from \( x = 0 \) to \( x_1 = 35 \, \text{cm} \). The spring constant then changes to \( k_2 = 250 \, \text{N/m} \) as the spring is stretched to \( x_2 = 65 \, \text{cm} \). 

From \( x_2 = 65 \, \text{cm} \) to \( x_3 = 89 \, \text{cm} \) the spring force is constant at \( F_3 = 105 \, \text{N} \).
Transcribed Image Text:### Problem 2 A certain spring has a spring constant \( k_1 = 660 \, \text{N/m} \) as the spring is stretched from \( x = 0 \) to \( x_1 = 35 \, \text{cm} \). The spring constant then changes to \( k_2 = 250 \, \text{N/m} \) as the spring is stretched to \( x_2 = 65 \, \text{cm} \). From \( x_2 = 65 \, \text{cm} \) to \( x_3 = 89 \, \text{cm} \) the spring force is constant at \( F_3 = 105 \, \text{N} \).
### Spring Force and Work Done: Problem Set

#### Part (c)
**Problem Statement:** Write an equation for the work done in stretching the spring from \( x_1 \) to \( x_2 \).

#### Part (d)
**Problem Statement:** Calculate the work done, in joules, in stretching the spring from \( x_1 \) to \( x_2 \).

#### Part (e)
**Problem Statement:** Calculate the work, in joules, necessary to stretch the spring from \( x = 0 \) to \( x_3 \).

### Notes:
- \( x_1, x_2, x_3 \) represent different positions along the spring's length.
- Ensure to use the correct formula for each calculation. For example, the work done to stretch a spring is generally found using \( W = \frac{1}{2} k (x_2^2 - x_1^2) \) where \( k \) is the spring constant.

No graphs or diagrams are provided with this problem set. Make sure to represent the spring's stretch algebraically and perform the necessary calculus if required.
Transcribed Image Text:### Spring Force and Work Done: Problem Set #### Part (c) **Problem Statement:** Write an equation for the work done in stretching the spring from \( x_1 \) to \( x_2 \). #### Part (d) **Problem Statement:** Calculate the work done, in joules, in stretching the spring from \( x_1 \) to \( x_2 \). #### Part (e) **Problem Statement:** Calculate the work, in joules, necessary to stretch the spring from \( x = 0 \) to \( x_3 \). ### Notes: - \( x_1, x_2, x_3 \) represent different positions along the spring's length. - Ensure to use the correct formula for each calculation. For example, the work done to stretch a spring is generally found using \( W = \frac{1}{2} k (x_2^2 - x_1^2) \) where \( k \) is the spring constant. No graphs or diagrams are provided with this problem set. Make sure to represent the spring's stretch algebraically and perform the necessary calculus if required.
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