Everyone knows I adulation both Star Wars and physics. I’ve been absent to do a physics column for Solo: A Star Star Wars Story—but I’ve waiting. I like to delay until the cine is accessible for home examination (online or Blu Ray) so that bodies accept a adventitious to watch it. If you haven’t apparent it yet, your time is up. You can accede this your SPOILER ALERT.
Actually, the being I’m activity to attending at in this column doesn’t absolutely absorb any aloft artifice points. It’s not like I’m activity to acknowledge that Darth Vader is Luke’s ancestor (oops—slight addle-brain active if you haven’t apparent The Empire Strikes Back). OK, actuality is your aftermost adventitious to bond on this physics post. You accept been warned.
Have you anytime noticed how some anchorage (particularly those bound curves on the avenue ramps) accept anchorage that aren’t level? There’s a acumen to add a coffer to these turns—they accomplish it easier for cars to about-face after crashing. Why?
Let me alpha with the analogue of acceleration. An article accelerates back it changes its velocity. If we attending at some abbreviate time breach (Δt), afresh the dispatch during this time breach would be authentic as:
But what the heck are those arrows aloft the “a” and “v”? Those arrows are there to announce that the dispatch and the dispatch are agent quantities. A agent is a blazon of capricious that has added than aloof one “piece” of information. A dispatch agent could accept three “parts”—a basic for anniversary ambit (since we alive in 3 dimensions). The aforementioned is accurate for acceleration—it has three components. So, it doesn’t aloof amount about the absolute dispatch but additionally the administration of that dispatch (which we alarm velocity).
The dispatch depends on the CHANGE in velocity—but the dispatch is a vector. This agency that aloof by alteration the administration of the dispatch (also accepted as turning) you accept an acceleration. Affective in a amphitheater at a connected dispatch is an acceleration. But dispatch is a agent too! The administration of the dispatch agent for an article affective in a amphitheater is appear the centermost of that circle.
Just to accomplish abiding aggregate is clear, actuality is a diagram assuming the top appearance of a car active in a amphitheater at a connected speed. You can see the car at two altered times with velocities in altered directions. I additionally put an arrow assuming the administration of the dispatch vector.
But how do you accomplish an article accelerate? In adjustment to accept an acceleration, you accept to accept a net force in the administration of the acceleration. So, if I accept a car axis in a amphitheater there has to be a force blame appear the centermost of the amphitheater (since that is the administration of the acceleration).
Here are two altered armament that could account a car to move in a circle. In both of these diagrams, the car is active appear the eyewitness and axis to the larboard of the screen.
For the car on the collapsed ambit (the one on the left), there is one force blame appear the centermost of the annular path—that is the frictional force. You charge abrasion amid the tires and the alley to get the car to turn. That’s why some bodies blast on icy roads—there’s not abundant abrasion to turn.
For the car on the banked turn, there is one big difference—it’s that force labeled FN. This is the force that the arena pushes up on the car and it’s erect to the arena (that’s why there is an “N” for normal). In this banked turn, the arena force does two things. First, it pushes up to annul the bottomward gravitational force. Second, it has a basic that pushes in the administration of the centermost of the circle. So this arena force is what causes the car to accept an acceleration. If you get the bend and the dispatch of the car aloof right, you don’t alike charge a frictional force to about-face the car. It doesn’t amount if the alley is wet, icy, or dry—it can still about-face with a banked road.
We accept this force-motion archetypal in physics. It says that the net force on an article is according to the artefact of accumulation and acceleration. But what is a force? A force is an alternation amid two objects—like back you advance on the wall, or back the Earth’s has a gravitational alternation with the moon. However, there is one affair about this idea—it alone works if you appearance things from a non-accelerating advertence anatomy (an inertial advertence frame).
What does this accept to do with Star Wars or axis cars? Well, accept you are in a car and that car makes a turn. Let’s say the car turns to the larboard and you are sitting in the commuter seat. How does it accomplish you feel? It feels like you are accepting pushed into the door, doesn’t it? It’s some airy force from this turn—except it’s not. There is no force blame you abroad from the turn. Instead, this is the ancillary of the car blame you IN to the turn. But back you are in the car and the car is accelerating, you accept put yourself in an accelerating advertence anatomy and the force-motion archetypal doesn’t work.
This is area we get to use affected forces. If you appetite to booty an accelerating advertence anatomy and accomplish it act like a non-accelerating anatomy you charge to accommodate affected forces. These affected armament are in the adverse administration of the dispatch of the anatomy and accomplish it so the force-motion archetypal works again. So that is a affected force blame you into the aperture of the car during a turn. Some bodies alarm it the “centrifugal force”—and that is accomplished as continued as you bethink that it’t not real.
Back to the cars on the collapsed and banked curve. Let’s add article in the car—some down-covered dice blind from the mirror. Back the car turns, there will be three armament on this down-covered dice (in the advertence anatomy of the accelerating car). In the car on the collapsed about-face there will be the bottomward force from gravity, and the accumbent force from the affected force blame abroad from the centermost of the circle. In adjustment to accomplish all the armament add up to zero, the cord captivation the dice charge cull at an angle.
What about the dice in the car on a banked curve? There is still a affected force blame abroad from the centermost of the circle. However, back the car is agee the gravitational force is not “straight down” (with account to the car). This agency the affected force can aish the alongside allotment of force and the dice hangs “straight down.” Here, maybe this diagram will help.
Notice that absolutely the blind dice are the aforementioned in both cars—it’s aloof the car acclimatization that’s different. From the angle of the banked axis car, it feels the aforementioned as admitting force was affairs “down” but aloof a little bit harder. There is no “sideways” force.
There is addition way to anticipate about the central of a axis car application the Equivalence Principle. Albert Einstien said that an accelerating advertence anatomy is duplicate from a gravitational field. This agency that if you are in a box with no windows and you feel your weight, this could be due to a gravitatational force OR because the box is accelerating.
With this idea, the central of a axis car is the aforementioned as a gravitational acreage that is the sum of the Earth’s gravitational acreage and the affected acreage from the acceleration. A car axis on a collapsed alley has a net agnate acreage that is askew to the attic such that things get pushed to the alfresco of the turn. A car on a banked about-face has the agnate gravitational acreage acicular beeline appear the attic so that you don’t move to the side, you aloof feel a little bit heavier.
We assuredly get to the arena in Solo: A Star Wars Story. In this allotment of the movie, it’s about a alternation robbery. But wait! This alternation is on an animated abuse and alike better, it leans on the advance back demography a turn. Han and Chewie are on the alternation during the about-face but it’s too late. The storm troopers arrive. The storm troopers are prepared. They accept alluring boots so they won’t abatement off the axis train. Chewbacca is not prepared. He about avalanche off—but his BFF is there to save him (BFF agency best acquaintance forever).
Here is my artisan arrangement of this scene.
Now you see the problem, right? If they are on a axis alternation that is on a banked turn, “down” would be appear the attic of the train, not the absolute down. Han doesn’t alike charge to save Chewie—physics can save him. Oh, and the storm troopers don’t alike charge alluring boots.
If the alternation was on a akin and axis track, THEN Chewbacca could be falling out and the storm troopers would charge alluring boots. But not for a turn. OK, I apperceive what you are saying. Yes, it is absolutely accessible that the alternation is on a banked clue that is not advised for that speed. If the alternation was activity too slow, afresh yes—the arena is absolutely correct.
Don’t get me wrong, I still like the movie. I aloof like physics also.
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