Physics behind parachutes

Physics:
For the egg not to break when it impacts the floor, its terminal velocity needs to be low enough, so that the egg’s skin can withstand the impact. That is, the parachute must decrease the egg’s terminal velocity enough for the impact with the floor to be weaker than what the egg’s skin can resist.
Terminal velocity is achieved, when the downward force of gravity is equal to the drag caused by the fluid in which the object is falling. In this case, the drag is doing a force upwards on the object. When the drag is equal to the force of gravity, there is no net force acting on the body and therefore there is no acceleration, leading to a constant velocity. This can be easily seen from the equation which connects force to acceleration:
it is obvious from this equation that when , .
Therefore, for this investigation, it is necessary to calculate the terminal velocity of the egg without a parachute and then, with the time taken of the different parachutes, compare and see which one did the best.

The density of air varies with temperature and therefore will be decided at the time of the experiment. The drag coefficient will also vary according to the shapes of the parachutes.
Using this equation it is possible to calculate the terminal velocity of the egg in the cup. Then with the terminal velocity, which will be the velocity it will hit the floor it will be possible to calculate the pressure which acts on the egg as it hits the floor. That is because the impact can be taken to an instant deceleration and that can be substituted into .
The area of the egg which hits the floor is then measured by drawing the parts of egg which touch a flat piece of paper. With this, the pressure acting on the egg can be calculated using .
The velocities of the falling eggs on different parachutes will be measured by timing the drop and measuring the height from which they are falling.

Following the equation above, the parachute which will result in the lowest terminal velocity will be that with the lowest density, that is, light weight and with a large surface area as its depth is almost negligible when calculating the density. The shape of the parachute will also affect its efficiency in slowing down the descent, as its drag coefficient will vary with its shape.