In Monday’s reference class, we looked at a variety of virtual reference interactions, and one of the example queries immediately grabbed my attention — because, of course, it was about physics! Unfortunately, it was part of an example of a horrid reference interview, but it did have me wondering: could I have answered the question if I had been the librarian at the desk for that patron? Let’s find out! It’s PAIGI (Physics As I Get It) time!
Here is the question: “When you drive forward in a bumper car at high speed and you slam into the car in front of you, you find yourself thrown forward in your car. Which way is your car accelerating?”
I admit, I am not as far into my independent physics studies as I would like, but that’s okay. I’ve already read a good bit about acceleration and the mechanics of objects in motion, so I’ll try to tackle this question with what I know already and supplement the inevitable gaps with research online.
Note: all definitions and equations, unless cited otherwise, are paraphrased from the fifth edition of W. Thomas Griffith’s “The Physics of Everyday Phenomena”.
This actually seems quite simple once broken down. I mean, bumper cars doesn’t seem like such an important factor as the patron seems to think it is. There is nothing mechanically special about bumper cars compared to, say, a SUV or a sports car that will make a huge difference in how they accelerate. The only main difference is that the bumper car can spin around in place in a 360 degree radius and has a large metal bar in the center like a stabilizer.
So here we are: is this a question about bumper cars or an object being acted upon by another force and its direction of acceleration? I’m going to wage it is the later not the former. This is like a lot of word problems in mathematics; the specific objects and scenarios are less important than the ideas and testable formulas behind them.
Let’s restate the question: “What direction does an object go when it collides at a high speed into another object?”
This seems like an issue of velocity, not purely acceleration. Acceleration is the rate as which velocity is changing. Velocity is a combination of an object’s direction of motion and how fast an object is going.
I see several issues with this problem already: we don’t know any information pertaining to either object’s speed, or what direction either object was going in at the time of collision (although I imagine that is less important). So we can’t calculate the object’s velocity. We also don’t know the makes and models of either car, err, object, so we cannot calculate the mass of either object. Nevertheless, we continue.
What we can do is look at a hypothetical momentum model that will tell us what direction either object would go into after a collision. Momentum is what you get when you multiply together the mass of an object and its velocity. The equation to figure out momentum is p = mv (I know, they use p as a stand-in for momentum, how confusing is that?!). Momentum is a vector quality. What does that mean? It means we might have to graph some stuff out.
Again, we are left with the same problem we’ve had before: our query doesn’t give us enough information. We return to the original query and see that outside of “bumper cars” it doesn’t give us much good data on the bumper cars’ weight or speed, other than they are going very fast, as bumper cars often do. Can we solve this question?
In this scenario, we spitball some numbers. We casually search for the average weight of a bumper car. Unfortunately, our top result and what looks like a very good niche source about this kinds of things presents another issue: there are different models of bumper cars! I had assumed all bumper cars were the same, but not all models have the bar keeping them aligned with the ceiling unit. There’s battery powered, adult size versus child size, inflatable versus rubber.
Being a beginner citizen scientist beholden to no particular STEM institution’s rules of ethics, I go “bugger it” and decide that the hypothetical bumper cars in the query are ceiling grid models and weigh 200kg. Now that we have decided our hypothetical bumper cars are the ceiling grid kind, we can use that to find out what their maximum speed is — again, I’m just guessing on speed here. But I imagine if the patron is thinking about one bumper car driver just flooring it into another, they are going as fast as their vehicle will allow.
And it is at this website that analyzes the physics of amusement park rides that I realize I’ve been needlessly complicating this query. Doh! Let us refer to Isaac Newton’s third law of motion, which the above blog references as well: “When one body exerts a force on a second body, the second body simultaneously exerts a force equal in magnitude and opposite in direction on the first body.”
Imagine bumper cars in action. One collides into another. There is the impact, the collision of equal forces against one another. There is, of course, a reaction to the action. They bump off each other and go on their way to collide into more cars. This is why you don’t really see bumper cars crumpled up around one another. This is why they’re called bumper cars and not hurling metal death traps on sticks.
There might be only one way to settle this: watch bumper cars in action, colliding into each other. Ladies and gentlemen, let’s go to the film!
In the video, after the collision, both bumper cars move forward. Momentum carries them both forward in the same direction. Their respective forces meet and react as appropriate to Newton’s third law. However, that is assuming that the car being hit in the query is also standing still! Just because the car is “in front of you” doesn’t necessitate that it is also stationary. In most bumper car collisions, one would assume both cars are moving. Would that change anything?
Fortune smiles on us. The same account that uploaded the above gives us a video that shows said scenario!
As we can see, once the cars collide into one another, they push away from each other in opposite directions. So the car going the high speed would be going backward, repelled by the other’s force. For every action, there is an equal and opposite reaction.
So. Which way is the car accelerating? Backwards. Perhaps not for a very long time – the driver will probably cut out of the backwards path to go veer at a different car – but right after collision the immediate acceleration path is behind, not forward. Why? Because both cars are, in that moment, exerting force upon one another, and that exertion of force sends it back to those objects – in this case, literally backwards. The reactionary force post-crash sends them skittering away from each other, like repelling magnets.
Is that the end of the query? It seems like it. We know what direction the bumper car is going and why. Maybe we could have given a more detailed answer if the patron had provided more specific information, like bumper car model and the speed of both objects, but for what we know, we did a good job (right?).
The problem for the patron is that they didn’t get to interact with a reference librarian who is familiar with Newton’s laws of motion, or physics in general. Maybe they would have had better luck in an engineering library? Unfortunately, even there, not every reference librarian is specifically trained to answer physics or STEM-related questions in a satisfactory way — and that is something I personally ran into during my last in-person reference interaction. We’ll talk about that in the next post!
PAIGI Comment Rule: If any of the above information or assumptions of answers are incorrect or would benefit from further extrapolation, please do not hesitate to comment and add on to the topic at hand! I only ask that you respect the level of physics learning I am still at – entry-level at best – and don’t be surprised if things are wrong or I ask questions about your comment that may seem obvious to you but not to myself. Thanks!