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Will your new MacBook crash to the ground without MagSafe? (Yes.)

Glenn Fleishman | March 13, 2015
Perhaps we should have read it as an omen that the MagSafe 2 adapter for older, original MagSafe connectors was listed as discontinued on the Apple Store in the U.S. and Canada last week. It's back in stock this week, but MagSafe's future in new Mac laptops is uncertain with the revelation of the single-port MacBook. With just a USB-C connection for power, data, and display, MagSafe may be on its way to sing with the choir invisible.

The MacBook exerts a pull of its own, just sitting there. We start with its mass, 2.03 lbs (0.92 kg), which would require a force of about 0.9N to accelerate it to 1m/s2. But we also have gravity in our world, and a so-called normal force must be calculated. Let's assume the MacBook is on a level surface. The earth exerts a pull of roughly 10m/s2 at the surface. We multiply that by 0.92 kg to get our force in newtons, or approximately 9N. (Aerospace engineer Bradley Grzesiak cautioned me to avoid too many decimal places: earth's gravity varies enough around the globe.)

But we have to factor in friction. Assume the rubber-footed MacBook — it has four feet, just like a MacBook Air — is on a wood table. A standard friction coefficient for rubber on wood, the closest comparison I could find, is 0.70 for static friction (sometimes called stiction), or friction at a standstill. Dr. Drang — the nom de Internet of a consulting engineer who writes exceedingly clever things about science, software, and engineering — suggested via email that 0.70 is optimistic for many surfaces, and 0.40 more reasonable.

Now we multiply the coefficient of 0.70 to get roughly 6N, or 0.40 to get about 4N. If the laptop is on a slick metal or glass table, the coefficient could be 0.20, or 2N or so. Consider gravity: this range of 2N to 6N is about 20 to 60 percent of one earth gravity. Not so much!

However, Grzesiak pointed me to a 1942 National Bureau of Standards (now NIST) testing report on rubber (see above) that looked with more detail into the initial point of overcoming static friction at various rates of initial acceleration. The higher the acceleration from zero velocity, the larger the coefficient.

A jerk from a cable could accelerate a laptop so rapidly that the initial coefficient factor of rubber on a glass table could be as high as 5 — meaning you'd need force on the order of five earth gravities (50N) to get the MacBook moving. But recall that force involves mass and acceleration: an abrupt yank by a heavy weight (like a human's leg intersecting with a cable) could briefly produce force on that order of magnitude!

After the laptop has overcome static friction, kinetic friction comes into play, dramatically reducing the force necessary to keep it in motion and accelerate it further.

A smashing good outcome

We have a lot of idealized and estimated starting conditions, so we can perform our thought experiments now. (I asked Apple for input, but didn't hear back.)

Let's take the case in which someone performs the most perfect pratfall such that the direction of force is absolutely and perfectly opposite the USB-C jack, so that there is no shear in any other orientation that we need to consider.

 

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