2. [-/1 Points] A spring has a spring constant value of 3300N/m. Determine the work needed to stretch the end of the spring, at a constant velocity, from x=3.6 cm to x=4.6 cm, where x=0 is the position of the spring at equilibrium (position where the spring is neither stretched or compressed), Helpful algebra reminder. a^2-b^2+(a-b)^2 square MY NOTES ASK YOUR TEACHER

To determine the work needed to stretch the end of the spring from \( x = 3.6 \) cm to \( x = 4.6 \) cm, we can use the formula for the work done on a spring:<br /><br />\[ W = \frac{1}{2} k (x_2^2 - x_1^2) \]<br /><br />where:<br />- \( W \) is the work done,<br />- \( k \) is the spring constant,<br />- \( x_1 \) and \( x_2 \) are the initial and final positions of the spring, respectively.<br /><br />Given:<br />- \( k = 3300 \, \text{N/m} \)<br />- \( x_1 = 3.6 \, \text{cm} = 0.036 \, \text{m} \)<br />- \( x_2 = 4.6 \, \text{cm} = 0.046 \, \text{m} \)<br /><br />Now, plug these values into the formula:<br /><br />\[ W = \frac{1}{2} \times 3300 \, \text{N/m} \times (0.046^2 - 0.036^2) \]<br /><br />First, calculate \( 0.046^2 \) and \( 0.036^2 \):<br /><br />\[ 0.046^2 = 0.002116 \]<br />\[ 0.036^2 = 0.001296 \]<br /><br />Next, find the difference:<br /><br />\[ 0.002116 - 0.001296 = 0.00082 \]<br /><br />Now, multiply by the spring constant and \( \frac{1}{2} \):<br /><br />\[ W = \frac{1}{2} \times 3300 \, \text{N/m} \times 0.00082 \, \text{m}^2 \]<br />\[ W = 1650 \, \text{N/m} \times 0.00082 \, \text{m}^2 \]<br />\[ W = 1.353 \, \text{J} \]<br /><br />Therefore, the work needed to stretch the end of the spring from \( x = 3.6 \) cm to \( x = 4.6 \) cm is \( 1.353 \) joules.