Hooke's Law
- Hooke’s law states that:
The extension of a spring is proportional to the applied force
- Where:
- F is the force applied
- k is the spring constant
- x is the extension of the spring
- The spring constant is the force per unit extension
- The units are N/m
- The spring constant is a measure of how stiff the spring is
- Directly proportional means that as the force is increased, the extension increases
- If the force is doubled, then the extension will double
- If the force is halved, then the extension will also halve
- The limit of proportionality is the point beyond which the relationship between force and extension is no longer directly proportional
- This limit varies according to the material
Hooke's Law states that a force applied to a spring will cause it to extend by an amount proportional to the force
Worked example
The figure below shows the forces acting on a child who is balancing on a pogo stick.The child and pogo stick are not moving.
The spring constant of the spring on the pogo stick is 4900 N/m. The weight of the child causes the spring to compress elastically from a length of 40 cm to a new length of 33 cm.
Calculate the weight of the child.
Answer:
Step 1: List the known quantities
- Spring constant, k = 4900 N/m
- Original length = 40 cm
- Final length = 33 cm
Step 2: Write the relevant equation
Step 3: Calculate the extension, x
Step 4: Convert any units
- Since the spring constant is given in N/m, must be in metres (m)
Step 5: Substitute the values into the Hooke's Law equation