Goal

Investigate conservation of energy by analysing a video of a water droplet falling.

Required data

Falling Water Drop Video

Useful information

• Surface area of a sphere of radius r = 4πr 2
• Volume of a sphere of radius r = (4/3)πr 3
• Surface area of a cylinder of radius r and height h = 2πr 2 + 2πrh
• Surface energy density of water/air = 0.073J/m 2
• Density of water = 1000kg/m 3

Preliminary questions

1. What is the surface area of a spherical water drop with a width of 20mm?
2. As a drop falls, it deforms, and its shape can be modelled as a cylindrical disk.  If the drop from question 1 spreads to a maximum width of 24mm and corresponding thickness of 9.26mm, what is the new surface area?
3. What is the change in surface area?
4. Molecules at the surface of a material have more energy than those in the material’s body; surface energy measures this “excess” energy.  Surface energy density describes the amount of energy required to create a surface of a certain area.
5. 1. What is the change in surface energy for the drop described above?
   2. Does the drop’s surface energy increase or decrease?
   3. Which shape (sphere or cylinder) is more energy-efficient?  What do you think the most energy-efficient shape is?  Why?