By Amanda C. Lee
In my last physics class, we were given the challenge of protecting an egg from a free fall drop. We were given parameters such as “devices must be free-standing” and “no materials can be attached to the egg (ie. it must be “naked”)”. Essentially, we would be dropping the egg onto our contraption to see if it cracks.
While designing our contraption, we looked for what would best cushion the egg’s fall. We thought of how if we dropped the egg into a pillow, it probably wouldn’t crack. To do this, we used the softest materials out of whatever we could find in the room.
We used a cardboard box to contain our chosen materials because of the box’s structural integrity. If the egg rolled after hitting the fabric, the idea was that it wouldn’t fall out and hit the ground. We then placed packing peanuts in the bottom of a cardboard box. This was done to reduce the chance of the egg cracking if it hit the firm box’s bottom. Then, loose fabric was placed on top of the packing peanuts to cushion the egg’s fall. With lots of fabric, the goal was to slow the egg to a stop before it hit the packing peanuts. We secured bubble wrap around the cardboard box to guide the egg into our contraption. The bubble wrap also served as a precautionary measure, in case the egg missed the box, or bounced out somehow.
Testing our contraption was a journey. We made it past the initial 0.5m drop, and kept going at heights increasing by 0.5m. Eventually, one of us had to stand on a table and drop the egg from the ceiling! Our egg did survive all the way up to a 3.0m drop, and may even have survived past that point; however, the height of the ceiling (and our own heights) restricted us from continuing. Our design worked so well because it lengthened the time that the egg took to stop moving. If two eggs are dropped from the same height, the egg that takes the longer time to stop will have a lower chance of cracking.
Taken from the equation Vf2 = Vi2 + 2ad, where Vf = final velocity, Vi = initial velocity, a = acceleration, and d = distance (height), we see that as long as the egg’s height, initial velocity, and acceleration remain constant, so will its final velocity. Then, looking at the equation Δp = mΔv = Fnett (impulse = mass • change in velocity = net force • time), we see that with the same mass and change in velocity, the impulse (change in momentum) of both eggs will also be the same. Thus, in order to reduce the net force acting on the egg, the time must increase.
Using the final velocity equation above, we see that as long as the egg’s initial velocity and acceleration remain constant, an increase in the height will also result in an increased final velocity. Since we are dropping the egg, we can guarantee that there will be an initial velocity of 0m/s and an acceleration due to gravity of 9.8m/s2. We have concluded above that a greater height = increase in final velocity and an increase in final velocity = greater impulse. Therefore, we can further conclude that an increase in height = greater impulse as well.
To improve the effectiveness of our design, we could make the cardboard box taller, and fill it with more fabric. Without changing the time it takes for the egg to stop moving, the net force acting on the egg would increase when dropped from greater heights. Therefore, in order to keep the net force low enough so that the egg doesn’t crack, we need to lengthen the time the egg is in motion for. Using more fabric and a larger box would effectively do this, thus protecting the egg from the greater net force caused by the egg’s greater impulse.
Real Life Application
Similar to an airbag, our device increases the amount of time that the egg takes to stop its momentum. Thus, its impact force spreads over a longer period of time. An airbag is designed the same way. Its goal is to protect the passenger from the harm that a greater impact force would cause. As mentioned above, if the time remains the same, a greater impulse would result in an increase in net force. In order to most effectively protect the egg, the time must be manipulated in order to decrease the impact force of the egg when it reaches 0m/s.