A pen contains a spring with a spring constant of 263 N/m. When the tip of the pen is in its retracted position, the spring is compressed by 4.8 mm from its unstrained length. This compression allows the pen to push the tip out when needed.
To understand how this works, let’s break it down. The spring constant is a measure of how stiff the spring is. In this case, a spring constant of 263 N/m means that for every meter the spring is compressed, it exerts a force of 263 Newtons.
When the pen’s tip is retracted, the spring is compressed by 4.8 mm, which is equivalent to 0.0048 m. Using Hooke’s Law, which states that the force exerted by a spring is equal to the spring constant multiplied by the displacement from its equilibrium position (F = kx), we can calculate the force exerted by this spring when compressed:
F = 263 N/m * 0.0048 m = 1.2624 N
This force is what propels the tip of the pen outward when you press down on the top of the pen. The mechanism is designed so that when the button is pushed, it releases the spring, causing it to expand and push the pen tip out, allowing you to write. This clever use of springs in writing instruments makes the pen easy to use and efficient.