Lesson summary
6.1.2 Hooke’s Law — AS PHYSICS 9702 notes: State Hooke’s law, use F = kx and find the spring constant from a force–extension graph.Statement — a material showing elastic behaviour obeys Hooke’s law if its extension is directly proportional to the applied force.Graph — the force–e…
- What the symbols mean
- Definition
- Reversed axes
- Limit of proportionality
- Compression
- Graph — the force–extension graph of such an object is a straight line through the origin
Section 1 of 6Hooke’s law
Statement
- Statement a material showing elastic behaviour obeys Hooke’s law if its extension is directly proportional to the applied force.
Graph
- Graph the force–extension graph of such an object is a straight line through the origin.
Equation
- F = kx.What the symbols mean: F = force (N) · k = spring constant (N m−1) · x or e = extension (m)
- F is the force applied in N.
- k is the spring constant in N m−1.
- x is the extension in m.
Section 2 of 6The spring constant
Meaning
- Meaning k measures the stiffness of a spring, and a stiffer spring has a larger k.
Definition
- Definition k is the force per unit extension up to the limit of proportionality.
Unit
- Unit the SI unit of k is N m−1.
Equation
- Equation k = F/x.
Graph
- Graph k is the gradient of the linear part of a force–extension graph.
Section 3 of 6Finding k from a graph
1
Check which quantity is on each axis.
2
Choose a large section of the straight line to find the changes in both axes.
3
Convert the extension to metres, for example from cm.
4
If force is on the y-axis, k is the gradient.
5
If the load F is on the x-axis and length is on the y-axis, the gradient is 1/k, so k = 1 ÷ gradient.
Section 4 of 6More from the specification
1Tensile forces and compressive forces
- Tensile forces and compressive forces materials deform elastically under external forces, with tensile forces causing extension and compressive forces causing shortening.
2Strain
- Extension per unit original length, ε = x/L.
3Stress
- Force per unit cross-sectional area, σ = F/A.What the symbols mean: σ = stress (Pa) · F = tensile force (N) · A = cross-sectional area (m2)
4Compression
- Decrease in length under a squashing force.
5Young modulus
- Ratio of stress to strain for a material, E = σ/ε.
6Compressive force
- Force that squashes a body and causes compression.
7Natural length
- Length with no force acting.
8Tensile stress
- Force per unit cross-sectional area, σ = F/A (Pa).
9Tensile force
- Force that stretches a body and causes extension.
10Reversed axes
- Reversed axes if extension is plotted against force, the gradient is 1/k, so the spring constant is the reciprocal of the gradient.
Section 5 of 6Key terms
| Term | Meaning |
|---|---|
| Hooke’s law | Extension is directly proportional to force provided the limit of proportionality is not exceeded. |
| Spring constant | Force per unit extension, a measure of stiffness, in N m⁻¹. |
| Limit of proportionality | Point where the force–extension graph stops being a straight line. |
| Stiffness | Resistance of a spring to deformation, measured by k. |
Section 6 of 6Exam technique
1
Taking the gradient as k when the axes are swapped — then k is 1 ÷ gradient.
2
Leaving extension in cm — convert to m for N m⁻¹.
3
Applying Hooke’s law beyond the limit of proportionality.
4
Thinking a stiffer spring has a smaller k — a stiffer spring has a larger k.