Why did my phone crack?

If you were to survey college students about the current state of their cell phones, you would likely find that a large portion of students have cracked phone screens. When asked how their phones broke you may hear a multitude of answers talking about how they dropped their phone face down and it broke. What is interesting however, is that I would bet most of the individuals with broken phones actually had dropped their phones many times before and no cracks resulted. This leads to the question as to why is it that I can drop my phone many times and it doesn't crack yet I drop it once and it cracks? What is it about the landing that causes phones to break sometimes and not others? The answer is rooted in physics obviously.

In class we have talked extensively about forces. If we look at the equation for force we find that it is equal to Pressure * Area. If we rearrange this formula we see that Pressure= Force / Area. From these equations we can see that Pressure and Area are inversely related which means that as Area increases, pressure decreases. Using these equations we can see why some falls are much more devastating to phone screens than others.

Based on company tests, it was determined that a phone screen can withstand 100,000 psi of pressure before cracking. With this in mind, we can look at how some falls with a low force upon impact can still produce 100,000 psi if it lands on a surface with a small area. For example, if we take an iPhone 11 which weighs 0.19kg and drop it from a height of 1 m such that it lands directly on its screen which has an area of 0.01125m^2, the screen only experiences a pressure of 24 psi if we assume the stopping distance is 1mm. If we were to shrink the impact area by a factor of 10000 (ie. it fell on a very very pointy rock or something) we would find that the pressure felt by the screen was 240000 which would cause the screen to break.

Moral of the story: Do not drop your phone screen down on a pointy rock or else it will break and that would really suck!