A 1.4kg falling object (subject to the effects of aerodynamicdrag) is 1800m high

Question

                                     A 1.4kg falling object (subject to the effects of aerodynamicdrag) is 1800m high, traveling at 34 m/s and has not yet reachedterminal speed. It first reaches                     terminal speed at a heightof 1340 m and the terminal speed is 37.3 m/s.                                                       a) How much thermal (internal) energy is generated through theaction of the drag force as the object falls from 1800m to1340m?                                                       b) Repeat a for the fall between 1340m and 500m.                                                       All solutions must be based on work and/or energymethods.                                                                    A 1.4kg falling object (subject to the effects of aerodynamicdrag) is 1800m high, traveling at 34 m/s and has not yet reachedterminal speed. It first reaches                     terminal speed at a heightof 1340 m and the terminal speed is 37.3 m/s.                                                       a) How much thermal (internal) energy is generated through theaction of the drag force as the object falls from 1800m to1340m?                                                       b) Repeat a for the fall between 1340m and 500m.                                                       All solutions must be based on work and/or energymethods.                                                   A 1.4kg falling object (subject to the effects of aerodynamicdrag) is 1800m high, traveling at 34 m/s and has not yet reachedterminal speed. It first reaches                     terminal speed at a heightof 1340 m and the terminal speed is 37.3 m/s.                                      a) How much thermal (internal) energy is generated through theaction of the drag force as the object falls from 1800m to1340m?                                      b) Repeat a for the fall between 1340m and 500m.                                      All solutions must be based on work and/or energymethods.                 

Explanation / Answer

The problem can be solved by using Conservation of Energy Theory.

Loss of Mechanical Energy = Air Drag Thermal Energy

a) Loss in Potential Energy = Change in Kinetic Energy + Air Drag Heat

1.4*9.8*(1800 - 1340) = (1/2)1.4(37.3^2 - 34^2) + Air Drag Heat

Air Drag Heat = 6146.5 J

b)In this case , there is no change in Kinetic Energy

Loss in Potential Energy = Air Drag Heat

1.4*9.8*(1340 -500) = Air Drag Heat = 11524.8 J

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