A force is an interaction between bodies described mathematically by a vector and measured in Newtons (N).
Types:
- Contact forces. A force between bodies in contact. Interactions are modeled with a step function ($\theta(r-a)$).
- Normal force, acting perpendicular on the surface
- friction force, acting parallel to the surface
- Tension force, caused by a stretched body (inner elastic forces)
- Short-range interactions. When the interaction decays exponentially with the distance ($\propto \exp{-\lambda r}$). They weaken very rapidly, so they are ‘first-neighbors’ interactions.
- Nuclear forces
- Ising model
- Long-range interactions. The interaction decays with a power law ($r^{-n}$). Forces act ‘at a distance’ so to speak.
- Gravitation
- Electromagnetic forces
#Superposition Principle
Multiple forces applied at the same point on a body have the same effect as a single force equal to the vector sum of the forces. This single force is called net force.
$$ \vec{F}_{net}=\vec{F}_{1}+\vec{F}_{2}+\vec{F}_{3}+\cdots=\sum \vec{F} $$ $$ F_{net,x}=\sum F_{x} \quad\quad F_{net,y}=\sum F_{y} \quad\quad F_{net,z}=\sum F_{z} $$Free-body diagrams
A free-body diagram consists of the following elements:
- A representation of the body on which Newton’s laws are applied.
- All the individual external forces acting on the body
- A coordinate system (conveniently chosen)
- accelerations can be included if needed as well.
When a problem involves more than one body, we can always draw a separate free-body diagram for each body
Equilibrium