# List of formulas related to Forces

## Attractive Forces

m1,m2: mass of two objects; r: distance between two objects; G: gravitational constant

$$F = G \frac{m_1 m_2}{r^2}$$ $$G = 6.67 \times 10^{-11} Nm^2 / kg^2$$

### Gravitational Force

M: Earth mass, m: mass of object, R: Earth radius, h: object’s height

$$F = G \frac{Mm}{(R + h)^2}$$ $$M \approx 6.67 \times 10^{24} kg$$ $$R \approx 6371 \times 10^{6} m$$

### Gravitational Acceleration

At a height h above the normal surface of the earth

$$g = \frac{Mm}{(R + h)^2}$$ $$\text{Near the sea level}$$ $$h << R => g_0 = \frac{GM}{R^2}$$

### Force Of Gravity

Force of gravity on earth, a special case of Gravitational force

$$P = G \frac{Mm}{(R + h)^2} = mg$$

### Newton's First Law

F: forces acting on the object , v: velocity of the object, a: acceleration of the object

$$\Sigma F = 0 => \frac{dv}{(dt)} = 0$$ $$a = 0$$

### Newton's Second Law

m: object’s mass(kg)

$$\xrightarrow[\text{F}]{} = \frac{d _{\overrightarrow{p}}}{d_t} = \frac{dm _{ \overrightarrow{v}}}{d_t} = m \frac{d _{ \overrightarrow{v}}}{d_t}$$ $$\xrightarrow[F]{} = m _{\overrightarrow{a}}$$ $${\xrightarrow[a]{}}= \frac{\overrightarrow{F}}{m}$$

### Newton's Third Law

$$\xrightarrow[F]{} _{BA} = \xrightarrow[F]{} _{AB}$$

### Linear Elasticity-Hooke's Law

K: spring constant (n/m), x: displacement(m)

$$F = -kx$$

A Mass suspended by a spring

$$F = P => k = \frac{mg}{x}$$

### Force of friction

µ: coefficient of friction, N: normal force

Fms = µN
= µPcosα
= µmgcosα