Forces and equilibrium
Forces and equilibrium
- A force is a vector (size + direction). Split it into components: horizontal $F\cos\theta$, vertical $F\sin\theta$.
- A particle is in equilibrium when the forces balance — the vector sum is zero (components add to zero in every direction).
Practice
A particle is in equilibrium when the forces on it:
Equilibrium means the forces balance — their vector sum is zero.
Practice
The horizontal component of a force F at angle θ to the horizontal is:
Horizontal component = F cos θ; vertical component = F sin θ.
Friction
- The contact force has the normal reaction $R$ (perpendicular) and friction $F$ (along the surface, opposing sliding).
- Friction grows only up to a maximum (limiting friction):
$$F \leq \mu R, \qquad F = \mu R \text{ at the point of slipping}$$
- where $\mu$ is the coefficient of friction.
Practice
The coefficient of friction is 0.4 and the normal reaction is 100 N. What is the maximum (limiting) friction force, in N?
Maximum friction = μR = 0.4 × 100 = 40 N.
You've got it
Key idea
- a force splits into $F\cos\theta$ (horizontal) and $F\sin\theta$ (vertical)
- equilibrium = forces balance (vector sum zero)
- friction $F \leq \mu R$, reaching $\mu R$ when about to slip