The laws of kinetic friction are,

1. The force of kinetic friction always acts in the opposite direction to which body is moving.
2. The force of kinetic friction remains constant for moderate speed but it decreases with an increase in speed.
3. Magnitude of kinetic friction has a constant ratio to normal reaction between two surface. The ratio of kinetic friction is slightly less than that in case of limiting force of static friction.
4. The coefficient of kinetic friction is independent of the area and shape of the contacting surfaces.

The formula for law of kinetic friction is given as,

F_K = µ_k N ——— where F_K =Force of kinetic friction, µ_k= coefficient of kinetic friction and N=Normal force

The formula for coefficient of kinetic friction is given as,

µ_k = F_K / N

The laws of static friction are,

• When two surfaces are in contact , the frictional force is always tangential to contacting surfaces in a direction opposite to that in which the body tends to move.
• The limiting force of static friction is directly proportional to normal reaction between two surfaces in contact.
• The force of static friction depends on nature and materials of surface.
• The coefficient of static friction is independent of the area and shape of the contacting surfaces.

The formula for law of static friction is given as,

  F_S = µ_s N      ——— where F_S=Force of static friction, µ_s= coefficient of static friction and N=Normal force

The formula for coefficient of static friction is given as,

µ_s = F_S / N 

If M is the mass of the earth, m is the mass of the body which is at the surface of the earth and R is the  distance between body and centre of the earth (which is the radius of the earth) . According to the Newton’s law of gravitation the gravitational force experienced by that mass m is given as,

F  =  G M m/R ²  ………………………(1)

As per Newton’s second law of motion, Force = mass × gravity = mg

Substituting value of force in equation 1 we get,

G M m/R ² = m g

The formula for Acceleration due to gravity at the surface of the Earth is given as,

g = G M /R ²

Where g =  Acceleration due to gravity, G = Universal Gravitational Constant, M = mass of the earth and R = radius of the earth

Every particle of matter will attract other particle of matter with a force that is directly proportional to product of mass and inversely proportional to square of the distance between them.

The formula for Newton’s law of gravitation is given as,

            F ∝ m₁ m₂ / r ²

Magnitude of Gravitational Force ( F)  =  G (m₁ m₂ / r ²)

Where G = Universal Gravitational Constant, m₁= mass of particle 1, m₂ = mass of particle 2 , r = the distance between the centers of the masses

The value of Universal Gravitational Constant(G) = 6.6733 x 10 ^-11 N . (m / kg)²

The Gravitational Potential Energy of a body at a point in a gravitational field is defined as the amount of work done in bringing the body from infinity to that point without acceleration.The gravitational potential energy at a point is always negative.

Mathematically,

Gravitational Potential Energy  = Gravitational Potential X mass of body (m).

Dimensional formula of Gravitational Potential = M⁰L²T^-2
Dimensional formula of Mass = M¹L⁰T⁰

Putting these values in above equation we get,

The Dimensional formula of Gravitational Potential Energy is M¹L²T^-2.
The SI unit of Gravitational Potential Energy is Joule (J).