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Gravity and Projectiles

Gravity and Projectiles. Let us start with a few questions. The discussion will bring out some interesting points which we often overlook. What is the vertical direction? Do heavier objects fall faster than lighter objects? how does the value of g vary when we go down inside the earth?

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Gravity and Projectiles

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  1. Gravity and Projectiles

  2. Let us start with a few questions. The discussion will bring out some interesting points which we often overlook. What is the vertical direction? Do heavier objects fall faster than lighter objects? how does the value of g vary when we go down inside the earth? What is the shape of the trajectory of a projectile?

  3. News Item on 21/07/2011 This morning at a missile test range the DRDO launched its first ever Prahaar missile that can strike within 10 m of a target 150 km away.

  4. What are the factors which can change the trajectory of a projectile? Gravity Centrifugal Force Variation of g with latitude RPOLE REQ REQ = 6378 km RPOLE =6357 km

  5. Combining variation of g with latitude and variation due to mass distribution inside the earth, scientists have derived the Geodetic Reference System for 1967

  6. Coriolis Force Earth is a rotating frame of reference. A body moving in this frame experiences a force called Coriolis force. This force causes a drift in the moving body to the right of its path. Expected vertical path Actual path A particle dropped from a height of 100 m suffers a deflection of only 0.0155 cm.

  7. A missile travelling with a velocity of 5000 km/hr, during its flight of 1000 s, will drift and miss its target by 100 km. Intended Path Actual Path

  8. Projectile with air resistance We all know that in the absence of any air resistance the path of a projectile is a parabola. y What happens to the path when air x resistance is taken into account?

  9. Suppose the object is a cricket ball bowled by a fast bowler at 144 km/hr (40 m/s). Resistance due to air is called air drag.

  10. y x

  11. The drag coefficient D depends on the area of the projectile facing the air in the direction of its motion and the density of air through which it moves. If A is the surface area of the projectile and ρ is the density of air, then drag coefficient can be written as

  12. The components of the velocity vector are The components of the drag force are

  13. The x- and y-coordinates advance to The new velocity found in Equations 6 is fed back into Equations 5 to get the new acceleration. Steps 5,6,7 and 8 are then repeated. The process is repeated a number of times and y is plotted against x to get the trajectory.

  14. The trajectories shown in the next slide have been plotted for a cricket ball travelling at a velocity of 40 m/s (144 km/hr) at an angle of 45º to the horizontal. The data was generated by a computer program. The mass of the cricket ball is taken as 0.160 kg and its radius as 0.0360 m (these are typical values). The value for the density of air has been adopted as 1.22 kg/m3, appropriate for sea level at 15 ºC.

  15. The values of the constant C are shown along each curve. We see that the resistance due to air cannot be ignored. Not only does the projectile not reach its expected height, its range is also considerably reduced.

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