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This is not an iPhone 6 Plus and I am not wearing skinny jeans (not yet).

Honestly, I think this whole bending of the iPhone 6 Plus thing is overblown. If you want, you could bend or break just about any electronic device. They aren't indestructible.

For me, the story isn't about the iPhone, instead it's about how people talk about the physics associated with a bending iPhone. Let's go over some of the commonly used phrases (and some that should be used).

Pressure vs. Force

Why do people wear snow shoes when walking through deep snow? Well, if you can stay on top of the snow instead of sinking down into it it makes it much easier to walk. The snow shoes increase the contact area of your foot as you take a step. The snow shoes do NOT change your weight.

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It turns out that the surface of the snow will "break" at some pressure and not at some particular force. Pressure is the applied force divided by the contact area. The units for pressure are Newtons per square meter – this is also called a Pascal. Another common unit for pressure is the psi – pounds per square inch.

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Snow shoes increase the area and thus decrease the pressure.

But what about bending an iPhone 6 Plus? It only partially depends on the contact area. Clearly if you push on a piece of aluminum (like the back of the iPhone) with a tiny little point, you can dent the back. But what about bending the whole phone? In that case, it doesn't depend on contact area except in the case where your whole hand is pushing on the back of the phone. In that case, you couldn't really bend it, could you?

One thing I'm not too fond of is the phrase "put some pressure into it". Maybe I'm just an old physicist that gets crotchety about these things. However, pressure is not a property of an object. It would be better to say it's a type of interaction. You could say apply pressure TO the phone. That might be better. I probably should just keep my mouth shut.

Force vs. Torque

Ok, so pressure maybe isn't the key thing to talk about when bending an iPhone (bendgate). What about force? Clearly if you push on a phone, it can have some type of effect. In general, a single force on an object will cause the object to change it's motion in someway. So, if you push on a phone but want it to stay in place, you will need a second force.

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Yes, you could push in a manner like this to crush your phone – but that's not what we are talking about. Instead, we want to look at some other case. Suppose we push on the phone like this:

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The net force on the object is still zero, but what about torque? What is torque? I like to describe torque as a rotational force. Just as forces change the motion of an object, the torque can change the rotational motion of an object. You can get a good example of torque when you open a door. Of course you have to push on the door, but the further you push from the hinge the easier it is to open the door. Thus torque depends on both the applied force and the distance this force is applied from some point.

In the above example, the torque on the phone is still zero. However, these torques can still do something to the object. In engineering (I am not an engineer – just saying), this is called the bending moment (Wikipedia). As far as I understand, the bending moment in the torque need to get an object to deform. It's not the net torque since that would be zero.

So, how does an object have forces applied to it and yet not bend? Actually, everything bends – even if just a little bit. When we say "bend" we really mean bend to the point where it doesn't come back. This happens when the internal stress in the material that makes up the object exceeds the yield strength of that material.

It's not quite the same thing, but here is a similar bit more detail looking at the torque and internal structure needed to keep a long oak tree branch horizontal.

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Image: Rhett Allain

I just think those oak trees are awesome.

Can Tight Jeans Bend Your Phone?

Maybe you just think skinny jeans are perfect for you and maybe you have the iPhone 6 Plus. You put your phone in your front (and very tight) pocket and later find that the phone is bent. What kind of torque could you get from a phone in jeans? Let's make a rough estimate.

Of course we should start with a diagram. Here is a side view of a phone in between your leg and a denim pant leg.

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Yes. That is a drawing my skin and it's purple. It's not a big deal – muppets have purple skin.

Now to calculate the bending moment. I think I am doing this right. If I know the tension (T) in the denim skinny jeans, the distance from the edge to the center of the phone (r), and the angle of the jeans (θ) then I calculate the magnitude of the torque from one side of the phone as:

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I can get a value for r – that's not hard. If I look at the long dimension of the iPhone Plus, then r would be 7.9 cm. What about the angle? I think if I estimate high, I could get a value of 10° (I'll admit that this is a total guess – it could be a larger angle). For the tension, that is tough. This site says the tension in Levi's can be up to 142 pounds. However, that is the tension that the jeans rip at (I think). Also, that is the tension in the whole thing – if I just have a smaller amount of material (like an an iPhone-ed size), I think the tension might be less.

Since I don't really know how they measure maximum bending moments, I am going to cheat. This very interesting article on the Verge shows the Apple iPhone testing labs. The author claims that Apple pushed with a force equivalent to 25 kg (about 250 N) in the middle of the iPhone (and I guess it didn't fail). So, what kind of fabric tension in skinny jeans would lead to the same middle force on the phone? In the iPhone lab tests, the two supports on the ends of the phone were pushing straight up. In the skinny jeans pockets, these forces are angled at 10°. So, in order to produce an upward force of 250 N from the thigh, the jeans would need a tension of 720 Newtons (162 pounds).

Let's consider the worst case scenario.  Suppose you have skinny jeans on a super skinny leg.  The leg is so skinny that when you put the iPhone 6 Plus in your pocket, the fabric pulls straight down at a 90 degree angle to the phone.  In this case, you would need 125 N tension in the fabric to be equivalent to the iPhone test in the lab.  That's only 28 pounds of tension, so you would think that would be ok.  But wait!  There are two problems.  First, some jeans can only take about 28 pounds of tension before ripping (not everything is Levi tough).  Second, the test at the Apple lab seemed to indicate that the iPhone could take an equivalent bending moment of 25 kg (250 N) at the center and that wouldn't make it bend.  How much does it take to bend?  Who knows.

What does this mean? This means that based on this estimate jeans would most likely tear before bending an iPhone 6 Plus. Remember, I said "based on this estimate". Yes, I know your friend Jimmy has a cousin who's sister's boyfriend actually bent his iPhone in his skinny jeans pocket. I got that.

Here's one last idea. Apple needs to send me an iPhone 6 Plus and a pair of skinny jeans. I will wear the jeans and use the phone for a week and then write a report on my experience. Apple, contact me.

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