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Basics of Mechanics

Equations of motion

V = u + at S = ut + ½ at2 v2 – u2 = 2as

Basic knowledge of Mechanics

  • Circular motion v = (2 (pi) r) / t
  • 0 net force & 0 acceleration does not mean 0 velocity
  • Centripetal force works towards the center = mv2 / r
  • Centrifugal force works wrt revolving body’s frame = Equal & opposite to centripetal force
  • Rolling Friction < Sliding friction
  • Friction is reduced by : Lubricants (as friction b/w Solid & liquid < b/w Solid & Solid), Ball bearings

F= m * a,     Momentum = m * v,   Work = F * distance moved in direction of force

Impulse = f * t = Change in momentum = Small contact time will lead to greater force

Power = WD/Time taken,   K.E = ½ mv2,    P.E = mgh        (Unit of KE & PE = Kwh)

1Kwh = 1000 w * 3600 s = 3600 *1000 J = 3600 Kj

  • Space rockets use liquid fuel + liquid oxygen (i.e. space rockets use its own oxygen to burn the fuel unlike jet engines which draws it from atmosphere)

Gravitational force = GM1M2 / r2     where G = 6.67 * 10-11 unit

Weight of a body is greater at poles than at equator mainly because of 2 reasons

  • Polar radius < Equatorial radius (Hence Greater gravitational force)
  • Greater centrifugal force at equator & 0 at poles

 

Weight of the body wrt Sea level

  • Weight of a body is less at higher elevations than at sea level, due to increase in radius
  • Weight of the body decreases as we move inside the earth & will be 0 at its centre as now gravitational force will act from all the sides
  • Mass of the body will be same everywhere as weight = m * g, hence it is weight that changes
  • Weight of a body at moon is 1/6 of that at earth

Weight of body at moon


Artificial Satellites

r = Distance from centre to earth

mv2 / r  = mg mv2 / r  = GMm/r2
v = (rg)1/2 v = (GM/r)1/2
  • Hence, speed of satellite does not depend on mass of the satellite
  • At a particular distance from the earth, all objects would have same speed of revolution
  • As v is inversely proportional to (r)1/2, when a satellite moves from higher to lower orbit, its speed will increase
  • Velocity of satellite = (6.4 * 106 * 9.8)1/2 ~ 8 km/s, Hence if v < 8 km/s, artificial satellite will fall to earth & if it is > 8 km/s, it will have elliptical orbit rather than a circular one
  • Escape velocity If v > 11.2 km/s, it will escape the earth & would never come back
  • Force of gravity (G) is minimum at equator, hence a better place to launch satellites & that too in west direction as earth moves W E
  • It is even easier to launch satellites from space shuttles due to no gravitational force

 


Geostationary Satellites

  • Satellites whose period of rotation is same as earth i.e. 24 hrs
  • Appears stationary with respect to earth
  • Mainly used for communication & weather forecast

 

Torque = Force * Perpendicular distance (Perpendicular from the line of action of force)

Center of Gravity = A point inside or outside the body where whole weight of the body is considered to act. For ex. Racing cars are built low with wide wheel base to keep COG as low as possible

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