A 1.4 kg falling object (subject to the effects of aerodynamic drag) is 1800 m high, traveling at 34 m/s and has not yet reached terminal speed. It first reaches terminal speed at a height of 1340 m and the terminal speed is 37.3 m/s. a) Determine if the mechanical energy ( � E = K +Ug ) of the system consisting of the falling object and Earth’s gravity field has been conserved during the fall from 1800 m to 500 m.

A 1.4 kg falling object (subject to the effects of aerodynamic drag) is 1800 m high, traveling at 34 m/s and has not yet reached terminal speed. It first reaches terminal speed at a height of 1340 m and the terminal speed is 37.3 m/s. a) Determine if the mechanical energy (
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E = K +Ug ) of the system consisting of the falling object and Earth’s gravity field has been conserved during the fall from 1800 m to 500 m. b) How much work (if any) including the correct sign (+ or -­‐) has been done on the system over this interval (presumably by the external drag force)? c) Will the energy of the system consisting of the object, the gravity field and the surrounding air be conserved over this interval? Explain your answer. Is there an additional energy that must be accounted for in this analysis? What is it and how much of it has been generated? Note: terminal speed is a constant speed.
48 kg diver jumps off a cliff (with a running start) into the ocean. The cliff is 50 m above the ocean below. Her coach, using a video of the dive, determines that at a point in flight when she has risen 0.7 m above the cliff, her speed1 (center of mass) is 0.5 m/s. Frictional effects such as drag are negligible. Formulate your solution using the diver and Earth’s gravity field as a system. Gravity does not do work on this system. It’s effects are captured in changes in potential energy. a) How much kinetic energy did she have at takeoff? What was her speed? b) How much kinetic energy will she have as she splashes into the ocean? c) What minimum amount of chemical energy needed to be consumed within the diver’s body in order for her to walk to the cliff, from ocean level, and then take off (jump)? Explain how you know.
1 Includes both x and y velocity components. This is not the highest point in the jump.