Day 14 - The Physics of Holiday Movies
The fun sponge is here to soak all the fun out of your favourite Christmas movies with physics 😂 Spoiler alert: everyone dies at the end!
National Lampoon’s Christmas Vacation
Ah, the infamous sledding scene. Clark rubs his saucer down with his company’s “non-caloric, silicon-based kitchen lubricant,” which supposedly creates a surface “500 times more slippery than any cooking oil.” Seconds later, he shoots off down the hill in a fiery blaze.
While Clark was onto something with his flying disc, maximizing the surface area exposed to the snow, unfortunately his teflon coating isn’t going to reduce the friction coefficient much more than what it already is. Assuming an absence of friction, in practice Clark would sail down the hill quickly, yes, but there’d be no fire! To accelerate as quickly as Clark does in the movie, something is either pushing him, or gravity is pulling him. If there’s an unseen rocket or some other hidden propulsion system pushing at Clark’s back, it could have caused his body to compress, potentially leading to internal injury - and a Christmas at the hospital.
Die Hard (yes, it’s a Christmas movie!)
Ever wonder if you could survive a hose pipe fall?! We’re breaking down the scene where our hero John McClane (played by Bruce Willis) makes his escape by jumping off the top of Nakatomi Plaza with nothing but a fire hose wrapped around his waist to break his fall! Very bold. Very Bruce.
Let’s consider the forces working on John. Die Hard Wiki (yes, it’s a thing) suggests Nakatomi Plaza is a 35-story skyscraper that is a total of 490 feet high. Looking at the clip, it looks like John falls 2-3 stories. So that ballparks us at 28-42 feet. We’ll split the difference and say 10m. Physics tells us that fall f=½gt², where g is the acceleration due to gravity, 10m/s² (yes, we’re rounding). So t=√(2 x f/g) = √(2 x 10/10) = √2 ~ so t is about 1.5 seconds.
Using v=gt, we can work out how fast (v) John is going just before the hose stops him. v=10x1.5=15m/s. Assuming John’s body mass (m) is around 70kg (remember, this is prime Bruce Willis) we can work out his energy from E=½mv². ½ x70x(15)²=7900J (Joules). For context, this is the sort of energy liberated when a very large firework explodes…!
Remember, as John is brought to a standstill all this energy has to be dissipated in the hose or in him. If this happens only at the very end of his fall he’s going to experience a much greater force than if he is brought to a stop over a longer braking distance. Since energy = force x distance (E = Fd), we can calculate the forces on John by rearranging. F=E/d (where d is the braking distance).
Being kind to John (he’s having quite the day, after all), pretend he uses a 5m bungee rope instead of the fire hose, and that this rope stretches another 5m to bring him to a gentle stop 10m below. Bungee ropes are made of many latex strands bundled together. Because of the elasticity of the strands they can absorb a great deal of the energy of a fall, making bungee jumps relatively safe. Using the formula we get a force on John of 7,900/5=1,580N (Newtons), equivalent to a weight of 158kg–roughly twice the weight of John McClane. It’s a bit like the force on your feet when you give someone a piggyback - that's not so bad!
Alas, he’s not using a bungee rope, he’s using a fire hose. Fire hoses are made of woven nylon, a masterpiece of chemical engineering. They can withstand pressures of up to 80 atmospheres (80 bar) pressures which, if the hose splits, can break a brick wall! Downside? These hoses are not very stretchy. If we assume the hose John uses stretches 1% (0.1m), F=7,900/0.1=79,000N–roughly 100 times John’s bodyweight!!! So what would happen to our action hero in reality? He dies. Hard. And Hans Gruber wins. Yikes.
Home Alone
If you thought Die Hard was good, just wait until you watch this exceptional video from Vsauce3 breaking down the absolutely devastating real life effects of Home Alone’s booby traps, which would have killed the Wet Bandits several times over!
The results of Jake Roper’s tests are horrifying to say the least. Don’t try Home Alone at home, kids. You might just kill someone.