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
