Which device exerts a force along its line of action and is proportional to its extension?

Which device exerts a force along its line of action and is proportional to its extension?

• A. Equilibrium Equation in Component Form
• B. Free Body Diagram
• C. String or Cable
• D. Linear Spring

Answer: (D)

This question highlights the idea of a restoring elastic force that acts along the device’s length and grows with how much it is stretched or compressed. A linear spring fits this description exactly: it exerts a force along its axis, and the magnitude is proportional to the extension from its natural length, described by Hooke’s law F = kx. Here, the force direction is along the line of the spring’s length, pulling when stretched and pushing when compressed, and its size increases linearly with the amount of displacement x. In contrast, a free body diagram is just a schematic of forces on a body, not a physical force-producing device. The equilibrium equation in component form is a method for summing forces, not a device that generates force. A string or cable transmits force along its length (tension), but for an ideal inextensible string the tension does not depend on extension; it’s not inherently proportional to how much the string has lengthened. If you treated the string as an elastic element, you’d need a different relationship, but the classical device that cleanly matches “force along its line of action and proportional to extension” is the linear spring.

This question highlights the idea of a restoring elastic force that acts along the device’s length and grows with how much it is stretched or compressed. A linear spring fits this description exactly: it exerts a force along its axis, and the magnitude is proportional to the extension from its natural length, described by Hooke’s law F = kx. Here, the force direction is along the line of the spring’s length, pulling when stretched and pushing when compressed, and its size increases linearly with the amount of displacement x.

In contrast, a free body diagram is just a schematic of forces on a body, not a physical force-producing device. The equilibrium equation in component form is a method for summing forces, not a device that generates force. A string or cable transmits force along its length (tension), but for an ideal inextensible string the tension does not depend on extension; it’s not inherently proportional to how much the string has lengthened. If you treated the string as an elastic element, you’d need a different relationship, but the classical device that cleanly matches “force along its line of action and proportional to extension” is the linear spring.