By Emily Golding ’14
On January 24th, the 2013-2014 Advanced Physics class dropped eggs on Dick Bradford’s head. Lucky for Dick, they were attached to a very specific number of rubber bands, calculated by students to drop a precise distance without cracking on Dick’s head. To find this number, we had to understand elastic potential energy and its relation to gravitational potential energy.Relating the equations for these two types of potential energy, after finding the length of one rubber band, the spring constant, and the distance from the drop height to the top of Dick’s head allowed us to solve for how many bands would be needed to get an egg as close to Dick’s head as possible without ruining his shirt.
As we had not tested our rubber band ropes with eggs attached, we were duly wary of the imminent danger to the head (pun not intended) of the upper school, and our first trials only came within around 20cm of Dick’s waiting pate. This large amount of error inspired us to to attempt the experiment again, lengthening our bungee cords with additional rubber bands. On the second trial, Dick still remained clean, but our re-calculations successfully brought the eggs well within the danger zone at 2.13cm.
m*g*h = 1/2 * k/n * ( h – nL)^2: Equation we derived relating elastic potential energy and gravitational potential energy.
Elastic potential energy: When something elastic, such as a rubber band or spring, is stretched (or compressed), it gains the capacity to perform work. Represented by half of the above equation: =1/2kx^2 (k=spring constant, x=distance stretched/compressed from equilibrium)
Gravitational potential energy: When an object is lifted so as not to be resting on the ground, when you let go, gravity is going to give it the capacity to do work. Represented by the other half of the above equation: =mgh (m=mass, g=gravitational acceleration, h=height from ground)
Spring constant: a number representing how stretchy the rubber bands are. Found with equation: f=kx (f=force applied, x=distance stretched/compressed from equilibrium)
Work: Energy transferred to or from an object by means of a force acting on the object.