A mass of 0.65 kg extends a spring by 12 cm. Calculate the constant. m^-1 0.054Nm^-1 53.08Nm^-1 0.55

Here's how to calculate the spring constant:<br /><br />**1. Understand the concept:**<br /><br />Hooke's Law states that the force exerted by a spring is proportional to its extension (or compression). Mathematically, this is represented as:<br /><br />F = kx<br /><br />Where:<br /><br />* F is the force applied (in Newtons)<br />* k is the spring constant (in Newtons per meter, Nm⁻¹)<br />* x is the extension (or compression) of the spring (in meters)<br /><br />**2. Identify the knowns:**<br /><br />* m (mass) = 0.65 kg<br />* x (extension) = 12 cm = 0.12 m (Important: convert cm to meters)<br />* g (acceleration due to gravity) = 9.8 m/s² (We need this because the weight of the mass is the force extending the spring)<br /><br />**3. Calculate the force:**<br /><br />The force extending the spring is the weight of the mass:<br /><br />F = mg = (0.65 kg)(9.8 m/s²) = 6.37 N<br /><br />**4. Solve for the spring constant (k):**<br /><br />Rearrange Hooke's Law to solve for k:<br /><br />k = F/x = 6.37 N / 0.12 m = 53.08 Nm⁻¹<br /><br />**Therefore, the spring constant is 53.08 Nm⁻¹.**<br />