"Forces and deformations: Hooke's law"
The spring in a ballpoint pen, the one in a trampoline and the one in a bathroom 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, 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. What mathematical formula relates the applied force to how much the spring stretches?
A spring has a spring constant $k = 10\ \text{N/cm}$, as shown in the figure. Calculate the force that must be applied to stretch it by $3\ \text{cm}$. Remember Hooke's…
A spring has a spring constant $k = 10\ \text{N/cm}$, as shown in the figure.
Calculate the force that must be applied to stretch it by $3\ \text{cm}$. Remember Hooke's law: $F = k \cdot x$.
A force of $20\ \text{N}$ is applied to a spring with constant $k = 5\ \text{N/cm}$. How many centimetres does it extend by?
A force of $20\ \text{N}$ is applied to a spring with constant $k = 5\ \text{N/cm}$. How many centimetres does it extend by?
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 motorbike, the first one deforms by several centimetres while the second barely moves. Which physical quantity measures this resistance to deformation that is particular to each spring?
Spring A has a spring constant of $k = 2\ \text{N/cm}$ and spring B has $k = 8\ \text{N/cm}$. Without performing calculations: a) Which one is "stiffer", that is, which…
Spring A has a spring constant of $k = 2\ \text{N/cm}$ and spring B has $k = 8\ \text{N/cm}$. Without performing calculations:
- a) Which one is "stiffer", that is, which one is harder to stretch?
- b) Which one will extend more if we apply the same force to both?
A spring extends by $4\ \text{cm}$ when a force of $2\ \text{N}$ is applied to it. Without doing detailed calculations, and considering Hooke's law: how much will it…
A spring extends by $4\ \text{cm}$ when a force of $2\ \text{N}$ is applied to it. Without doing detailed calculations, and considering Hooke's law: how much will it extend with $4\ \text{N}$? And with $1\ \text{N}$? Justify your answers.
A spring has a spring constant of $k = 200\ \text{N/m}$ and extends by $5\ \text{cm}$. a) Express the extension in metres. b) Calculate the applied force.
A spring has a spring constant of $k = 200\ \text{N/m}$ and extends by $5\ \text{cm}$.
- a) Express the extension in metres.
- b) Calculate the applied force.
The newtonmeter: a spring for measuring forces
What is a newton meter? What quantity does it measure and in which unit? What is the main part inside it?
What is a newton meter? What quantity does it measure and in which unit? What is the main part inside it?
When a weight of $8\ \text{N}$ is hung from a spring, it extends by $2\ \text{cm}$, as shown in the figure. Calculate the spring constant of the spring, in $\text{N/cm}$.
When a weight of $8\ \text{N}$ is hung from a spring, it extends by $2\ \text{cm}$, as shown in the figure.
Calculate the spring constant of the spring, in $\text{N/cm}$.
When a force of $10\ \text{N}$ is applied to a spring, it extends by $5\ \text{cm}$. a) Calculate its spring constant. b) What force will be required to extend it by…
When a force of $10\ \text{N}$ is applied to a spring, it extends by $5\ \text{cm}$.
- a) Calculate its spring constant.
- b) What force will be required to extend it by $8\ \text{cm}$?