WORK, ENERGY AND POWER

 

Work = F s Cos q where q is the angle between force (F) and displacement(s).

 

Translational kinetic energy of a body of mass ‘m’ and velocity ’v’ is

K.E = ½ mv²

 

Rotational kinetic energy of a body of moment of inertia ‘I’ and angular velocity  is

K.E_rot= ½ I²

 

Gravitational Potential energy = mgh, where h is the height with respect to some               

                                                               reference point

Elastic Potential energy of a spring = ½ kx2, where k is the spring constant,

x is displacement from         equilibrium position

 

Power is the work done per unit time.

P =

Instantaneous Power =  = F.v

                                                        GRAVITATION

 

Newton’s law of Gravitation If m₁ & m₂ are the masses separated by distance r, then the force between them is

F =, G is universal Gravitational constant = 6.67 x 10^-11 Nm²/kg²

 

Acceleration due to gravity at a distance r from the centre of a planet of mass M is

g =

 

Gravitational Potential at a distance r in the gravitational field of mass M is

V =

 

Orbital velocity of a satellite at a height h from a planet of mass M and radius R is

v_o=

 

Escape velocity of a body from the surface of a planet of radius R and mass M is

ve=