Do I Really Need a Case for My Iphone5?

By Danielle Glassman

Back-story! I am really clumsy and drop everything. I needed a new phone and decided that I wanted an Iphone 5, but I was scared that it would break when I would drop it. When I got my phone I forgot to get a case, so I ordered a speck case online. In the meantime, I kept my phone in a sock. During the two-week waiting period for my case to arrive, I was insanely overprotective of my phone. Now looking back on it, I question if I needed a case in the first place. I found this video online of iphone5 drop tests and used physics to see if I really need a case.

http://www.youtube.com/watch?v=pMvE0lkunBg

Iphone screen is composed of…

To make the calculations and comparisons easier I focused on the glass substrate as being the main component of the screen. I looked up the young’s modulus to be Young’s Modulus of Glass is 50-90 GPa so estimated ~70 X 10^6 Pa

The body is composed of anodized aluminum. I looked up the young’s modulus of it to be 26.9 GPa so ~27 x10^6 Pa. It was chosen because it is durable, light-weight and can be painted any color.

Measured depth screen- 0.1cm

Measured width screen- 5.5 cm

Cross-Sectional Area of Iphone5 Screen- 0.000055m²

Measured width body- 5.5 cm

Measured depth body- 7.6mm

Cross-Sectional Area of Iphone Body- 0.000418 m²

Estimated height of man to be 5 ft 11 inches or ~1.8 meters

Heights of Drops

Lap- 0.5 meters

Pocket- 0.6 meters

Shoulder- 1.6 meters

Head- 1.8 meters

Above Head- (add 0.5 meters) 2.3 meters

Using equation for tensile stress: F/A= E ΔL/ Lo

I calculated the amount of force exerted on the Iphone at the different drop heights for the body of the phone and the screen

Position of Drop	Force on Body (N)	Force on Screen (N)
Lap	5643	192.5
Pocket	6772	231.0
Shoulder	18058	6160
Head	20315	6930
Above Head	25958	8855

In all of the drops the screen was unharmed and the body of the phone was dented after the shoulder height.

Do I have to be concerned about denting the body of the phone?

YES if I drop the phone from the height of my head.

NO If I drop it from where my pocket is (~0.8meters) exert a force of 9029N, which is less than that of the shoulder.

Therefore, assuming that the time I would drop my phone the majority of the time from a height around my pocket, my calculations lead me to believe that I would not need a phone case. However, at times when I drop my phone I tend to be on elevated surfaces, so having a case could be useful. In the end, my phone case is more aesthetically pleasing than protective.

Note: I could have been off in my calculations and estimated the total height of the man wrong, which would alter the rest of the height calculations. This could impact if I drop the phone from my maximum height of my head if I will dent the case or not. However, that is irrelevant as I mainly drop it when I                                                                    am using it at pocket level.