The spring in a ballpoint pen, the one in a backyard trampoline and the one in a fishing scale have something in common: the harder you pull on them, the more they stretch. And if you pull twice as hard, they stretch twice as much. This simple relationship has a name of its own: Hooke's law.
A spring stretches in proportion to the force
If you hang weights of $1\ \text{N}$, $2\ \text{N}$ and $3\ \text{N}$ from the same spring in the lab, you find that it stretches $1.5\ \text{cm}$, $3.0\ \text{cm}$ and $4.5\ \text{cm}$: each newton added always produces exactly the same extension. Hooke's law says the extension of a spring is directly proportional to the force applied to it. What mathematical formula relates the applied force to how much the spring stretches?
The spring constant: "stiff" and "soft" springs
If you hang the same $5\ \text{N}$ weight from the thin spring of a ballpoint pen and from the thick spring of a motorcycle, the first one deforms by several centimeters while the second barely moves. Which physical quantity measures this resistance to deformation that is particular to each spring?
The newton meter: a spring for measuring forces
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What is a newton meter (also called a spring scale)? What quantity does it measure and in which unit? What is the main part inside it?
What is a newton meter (also called a spring scale)? What quantity does it measure and in which unit? What is the main part inside it?
We hang a bag of oranges from a newton meter and it reads $15\ \text{N}$, as shown in the figure. a) What force is the newton meter measuring? b) The bag is stationary:…
We hang a bag of oranges from a newton meter and it reads $15\ \text{N}$, as shown in the figure.
a) What force is the newton meter measuring?
b) The bag is stationary: what force does the newton meter exert on the bag?
Hooke's law does not work forever. If you stretch a spring too far, it will not return to its original length when you let go. How can you tell, from a table or a graph, where the law stops working?
On a force–extension graph, Hooke's law gives a straight line through the origin. Its slope is $F / x = k$, so a steeper line means a stiffer spring. At the elastic limit the line starts to bend.
Summary
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