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1 - Science of Physics
2 - Forces and Motion      Chapter 2 at a glance      2.1 - Motion      2.2 - Force, momentum, and Newton's laws      2.3 - Circular motion      2.4 - Solving harder physics problems      2.5 - Chapter review3 - Energy Transformations4 - Waves and Sound
5 - Electricity and Magnetism
6 - Light and Optics
7 - The Atom
8 - Linear Motion
9 - Vectors and Forces
10 - Forces
11 - Newton's Laws and Gravitation
12 - Circular Motion and Gravitation
13 - Torque and Static Equilibrium
14 - Momentum and Collisions
15 - Angular momentum
16 - Power and Machines
17 - Harmonic Motion
18 - Waves
19 - Sound
20 - Electricity
21 - Electric and Magnetic Fields
22 - Electromagnetism and Induction
23 - Light and Color
24 - Geometrical Optics
25 - Electromagnetic Radiation
26 - The Properties of Matter
27 - Thermodynamics and Heat Transfer
28 - The Atom
29 - The Quantum Theory
30 - TBD
31 - TBD
32 - TBD
33 - TBD
34 - TBD
35 - TBD
36 - TBD
37 - The atomic nucleus and radioactivity
38 - Nuclear reactions
39 - Relativity
40 - Particle physics and the standard model
41 - Electronics (semiconductors)
42 - Nuclear technology
43 - Lasers and photonics
44 - Metals, alloys and materials science
45 - Communications technology
46 - Buildings and structures
47 - Energy technology
48 - Biophysics
49 - Matter and Energy, Space and Time
50 - Energy Transformations
51 - Nanotechnology
52 - Website Videos
53 - ExtraStuff
55 - Modeling Motion, Friction, and Center of Mass
56 - Work and the Conservation of Energy
Springs and Hooke's law
How do springs work? A spring is a device specifically created to provide controlled amounts of force in many applications. The force exerted by a spring depends on how much it is deformed from its free length. The free length is the length of the spring when it is not exerting any force. The farther the spring is extended or compressed from its free length, the stronger the force the spring it exerts on whatever is causing it to extend or compress.
Compression, extension, and torsion springs
Hooke's law The restoring force for a spring is proportional to the deformation, x of the spring relative to its free length. If you deform an ideal spring twice as far, it will produce twice the force. This relationship is known as Hooke's Law, and is mathematically expressed as equation 2.8. Note: the force F in equation 2.8 is the force that the spring exerts, not the force exerted by whatever deforms the spring, such as your hand.
Hooke's law calculator
(2.8) F=−kx
F  = restoring force (N)
k  = spring constant (N/m)
x  = displacement from equilibrium (m)
Hooke's law for springs
What is "k"? Suspension of a car The quantity k is called the spring constant, which is the ratio of the magnitude of the force divided by the amount of deformation. The spring constant has units of force divided by distance. A spring constant of 1 N/m means the spring creates a force of one newton when stretched one meter. A stiff spring deforms very little, even under a large force and may have a value of k = 100,000 N/m or higher. A loose spring takes very little force to deform and may have a value of k = 100 N/m or less. The spring constant is different for every spring.
Why is there a negative sign in Hooke's law? The negative sign in equation 2.8 tells you that the force exerted by the spring acts in the opposite direction from the deformation. If you stretch the extension spring in the diagram above, the deformation, x, is positive. The force is negative indicating that it is to the left, opposite the deformation. If the deformation is negative, to the left, then the force is positive, to the right. Be careful when using Hooke's law to use the proper sign for the deformation, x.
Test your knowledge A spring with a spring constant of 50 N/m is displaced −0.8 meters. What is the force exerted by the spring?
  1. 50 N
  2. 40 N
  3. 20 N
  4. 60 N
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