Falling Speeds: Account for Energy in a Fall

Compare an ideal energy conversion with a fall that includes drag.

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Near Earth with constant g, lost gravitational potential energy is mgh. Without drag, a rest-start fall gives mgh = mv^2/2. With drag, some energy is transferred to the surroundings and internal energy, so kinetic gain is smaller.

Worked example

For m = 2 kg, g = 10 m/s^2 and h = 1 m, the potential decrease is 20 J. If 8 J is transferred by drag, kinetic energy becomes 12 J and speed is sqrt(12) m/s, about 3.46 m/s.

A model energy budget starts with 20 joules of gravitational potential energy. With drag, 12 joules become kinetic energy and 8 joules are transferred to the surroundings and internal energy.

Would you believe it?

An object at steady terminal speed is still losing height. Its kinetic energy stays unchanged while energy is transferred to the air and internal energy through drag.

OpenStax: energy conservation

Question 1 What is the potential-energy decrease? 2 J 20 J 10 J

Question 2 After an 8 J drag transfer, what kinetic energy remains? 12 J 28 J 8 J

Question 3 For mass 2 kg and kinetic energy 12 J, speed is approximately what? 6 m/s 12 m/s 3.46 m/s

Question 4 Has the 8 J been destroyed? Yes, energy has no conservation rule No, it was transferred into other energy stores Yes, drag destroys energy

Question 5 At steady terminal speed, lost height energy does what? Transfers without increasing kinetic energy Builds up as greater speed Disappears with no destination

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