In 2006, Apple produced laptops with the MagSafe power adapter. The idea is that the power plug that goes into the laptop is connect with a magnet instead of the usual plug in hole type thingy (surely there is also a technical term for this). Why would you want a magnetic power cord? Well, if you trip over the cable, the MagSafe just pops off. It saves your computer from falling off a table by using a magnet – thus MagSafe.
The most recent MacBook does not have a MagSafe power plug. Instead, it is charged over USB-C. In fact, there is only one port on the MacBook and that it is a USB-C. It’s kind of a cool idea. If USB-C was more popular, you wouldn’t have to worry so much about charging your laptop. Surely you could find a USB-C plug somewhere. Although USB-C charging is an interesting idea, it comes at a cost – no more MagSafe.
So, how safe is MagSafe anyway? This MacWorld post has some answers – but I like to collect my own data.
Coefficient of Friction
The first thing to look at is the force needed to pull a laptop off a table. Suppose I give the power cord a tug. Here is a diagram showing the forces on a laptop.
If the laptop stays at rest, these 4 forces must add up to the zero vector. Just to be clear, we have the following 4 forces:
The gravitational force.
The tension in the power cord pulling on the laptop (labeled T).
The force the table pushes up on the laptop. We usually call this the normal force so I am using an N for it.
Finally, the friction force.
The usual model for the frictional force says that the maximum magnitude of this force is proportional to the normal force and some coefficient of friction. I can write the following expression for the magnitude of the frictional force.
The coefficient of friction (μ) depends on the two types of materials interacting. The bottom of the MacBook usually has these rubber pads and then the table could be wood or metal or whatever.
In order to find the coefficient of friction, I need to do a simple experiment. Of course, you could do a much more complicated experiment, but let’s keep it simple for now.
If I pull horizontally on a laptop and measure the force right when it starts to slide, the coefficient can be found as:
That’s not too difficult. All I need to do is to pull the computer.
This is my first method. I folded over a piece of duck tape and stuck it in between the screen and keyboard. Then I just pulled with a low-tech spring scale. With this, I could test different surfaces such as tile board (we use these for dry eraser markers) or a desk.
The only problem with the spring-scale is that it’s a little difficult to get the force reading at the moment the laptop slides (you can do it – it’s just tough). As a check, I decide to use a force sensor along with a position wheel. This allows me to get force vs. position data. Here is what the data from that would look like.
In the darker data, the laptop slid when I pulled with a force around 9 Newtons. For the other run, the duck tape slipped a little bit but I can still get an estimate for the maximum frictional force. Also, I found two different laptops to test. One is an older 15 inch MacBook Pro and the other is a newer 13 inch MacBook Pro.
The error bars in these bar graphs are just the standard deviations from the multiple friction pulls. I’m a little surprised that there a appears to be a difference in coefficients for the 13 inch and 15 inch MacBook Pro. I figured that since they have the same type of “feet” they would have similar coefficients. Oh well. Also notice that I only test three different surfaces. Really, there are tons of different surfaces that you could put your computer on. From this data, I am just going to use an approximate coefficient of static friction around 0.35.
Pulling a Plug
How much force does it take to pull out a USB cable? What about a MagSafe power adapter? Yes, I could just hook up a force probe and pull it, but that wouldn’t be much fun. Also, I don’t think it would tell the whole story. For instance, an Apple brand USB cable (like the cable for an iPhone) takes about 5 Newtons to pull it out. The MagSafe takes over 20 Newtons to pull out. So, which is better? The answer, the MagSafe. Why? The USB is easier to pull out if you pull it straight out but the MagSafe is easier to pull out at an angle. If you have a laptop on a table and someone kicks the cord, I doubt it would get pulled straight out. Ok, here is a plot of the force to remove vs. angle (where 0° is pulling it straight out).
I tried two different USB cables. One was some random black cable and the other was the Apple. I also tested the iPhone lightning cable. I admit that I didn’t collect too much data on the lightning cable. I find that these suckers break too easily on their own and didn’t need any help from my science experiment. However, you can still see the important point: the MagSafe is easier to remove at greater angles and the other cables are more difficult to remove at greater angles.
Oh, what about the 15 inch MacBook Pro? I really didn’t get very good angle data on that one. It has an adapter that makes it essentially impossible to pull straight out. Here’s a closer look.
Of course I still pulled this plug, it’s just that the angle was difficult to define. The removal force for this side entering MagSafe was between 2.5 and 12 Newtons. Really, this plug seems like the best design. I don’t know why the newer MacBooks have the straight on style plug.
How to Break Your Computer
You can pull on your power cable and two things can happen.
The force can be greater than the plug removal force and the plug comes out.
The force can be less than the removal force and greater than the static friction force. The laptop starts slide. It might be time for an upgrade.
The force is less than the removal force and less than the static friction force. You just pull and nothing happens. Get back to work.
If I use a coefficient of friction of around 0.35, it would take a pulling for around 7-8 Newtons to get a laptop sliding. Looking at the removal force graph above, you can see that a cable angle of around 10-20 degrees will result in a removal force over 10 Newtons – well except for the MagSafe which goes the opposite way and has the lowest plug removal force at a angle greater than 20 degrees.
Oh, the iPhone is pretty much screwed. The iPhone 6 Plus has a mass of only 0.172 kg. If it has a similar coefficient of friction it would only need a pulling force of 0.6 Newtons. That lightning connector isn’t going to come out by itself. Of course you probably know that you can lift an iPhone just by the cable.
So here is how to NOT break your computer (unless you need an excuse to upgrade). First, don’t trip over your power cord. But if you do, make sure the cable comes out straight and not at an angle. Second, use the MagSafe – it’s better.
Of course there are still questions left unanswered.
If you pull real hard, would it make the laptop turn in such a way that the cable entry angle changes? Maybe this will help it come out.
Also, if you pull real hard the laptop will accelerate. I really need to look at force as a function of both time and position for an accelerating laptop.
What if you pull UP on the cable? This would have a similar effect on the removal force, but it would change the normal force (and reduce the frictional force). What is the lowest force case for sliding a laptop?
I didn’t look at kinetic friction. You can do that.
Although I measured the removal force for the Apple Lightning connector, I didn’t look at the coefficient of friction for an iPhone. There are just too many different cases that you could use to make the coefficients different. If you want to investigate this, have fun.
Finally, I am really missing some data on the USB-C. I think the only way to solve this problem is for Apple to send me a new MacBook to test. Apple, send me an email and I can give you a shipping address.
