To stretch a spring 9,3 cm from its unstretched length, 23,8 Jof work must be done . What is the stifness constant (spring constant) of this spring in N/m ? (in N) Round off your result to 1 decimal place. Yanit: square

To find the stiffness constant (spring constant) of the spring, we can use Hooke's Law, which states that the force required to stretch or compress a spring by a distance x is proportional to that distance. Mathematically, this is expressed as:<br /><br />\[ F = kx \]<br /><br />where:<br />- \( F \) is the force applied,<br />- \( k \) is the spring constant,<br />- \( x \) is the displacement from the unstretched length.<br /><br />The work done to stretch a spring is given by the equation:<br /><br />\[ W = \frac{1}{2} k x^2 \]<br /><br />where:<br />- \( W \) is the work done,<br />- \( k \) is the spring constant,<br />- \( x \) is the displacement from the unstretched length.<br /><br />Given:<br />- \( W = 23.8 \) J,<br />- \( x = 9.3 \) cm = 0.093 m (since 1 cm = 0.01 m).<br /><br />We need to solve for \( k \):<br /><br />\[ 23.8 = \frac{1}{2} k (0.093)^2 \]<br /><br />First, calculate \( (0.093)^2 \):<br /><br />\[ (0.093)^2 = 0.008649 \]<br /><br />Now, substitute this value back into the equation:<br /><br />\[ 23.8 = \frac{1}{2} k (0.008649) \]<br /><br />Multiply both sides by 2 to isolate \( k \):<br /><br />\[ 47.6 = k (0.008649) \]<br /><br />Now, solve for \( k \):<br /><br />\[ k = \frac{47.6}{0.008649} \]<br /><br />\[ k \approx 5540.6 \]<br /><br />So, the stiffness constant (spring constant) of the spring is approximately \( 5540.6 \) N/m.