Ep. 314: Acceleration

Put that pedal to the metal and accelerate! It’s not just velocity, but a change in velocity. Let’s take a look at acceleration, how you measure it, and how Einstein changed our understanding of this exciting activity.

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This episode is sponsored by: 8th Light, Swinburne Astronomy Online

Show Notes

  • Cosmos Trailer
  • Acceleration — Physics Classroom
  • Basic Properties of Vectors — GSU
  • Difference between centripetal and centrifugal forces — Washington University
  • How Fast are you Moving When You are Sitting Still? — Universe in the Classroom
  • The Acceleration of Gravity — Physics Classroom
  • Galileo’s Acceleration Experiment — UVa
  • Experiment: Conservation of Energy and Projectile Motion — Harvard (pdf)
  • Twin Paradox and other special relativity experiments — GSU
  • Kinetic Energy — GSU
  • Transcript

    Transcription services provided by: GMR Transcription

    Female Speaker: This episode of Astronomy Cast is brought to you by Swinburne Astronomy Online, the world’s longest running online astronomy degree program. Visit Astronomy.swin.edu.au for more information.
    Fraser Cain: Astronomy Cast episode 314 from Monday, July 8th, 2013. Acceleration. Welcome to Astronomy Cast, our weekly facts based journey through the cosmos where we help you understand not only what we know but how we know what we know. My name is Fraser Cain. I’m the publisher of Universe Today and with me is Dr. Pamela Gay, a professional at Southern Illinois University Edwardsville and the director of CosmoQuest. Hey, Pamela. How you doing?
    Pamela Gay: I’m doing well. How are you doing Fraser?
    Fraser Cain: Good. I’m enunciating very carefully after messing up the first intro and we had a few technical problems getting this episode rolling. So now, I’m walking on pins and needles. Hey, have you seen the trailer for the new Cosmo show yet?
    Pamela Gay: No.
    Fraser Cain: Out favorite person in the world, Neil deGrasse Tyson is doing a recreation of Cosmos from Seth from the Family Guy and it looks awesome. It really looks amazing and I can’t wait to see it. They ran the trailer at Comic Con and it looks just phenomenal.
    Pamela Gay: Yeah. I’ve been working my butt off over here and I’m highly amused because Netflix keeps sending me emails reminding me that I have an account. “Use it.” And it’s like, “No.”
    Fraser Cain: That’s sad.
    Pamela Gay: So nothing –
    Fraser Cain: That’s pathetic.
    Pamela Gay: Exists except for the work I’m doing right now.
    Fraser Cain: Well, when this is over, go search for the new Cosmos trailer and watch it and I think you’ll be pleasantly impressed.
    Pamela Gay: Okay.
    Fraser Cain: The fact that it doesn’t have enough Fraser and Pamela in it is a problem. Apart from that, it just looks amazing. It’s on Fox. What a crazy time we live in. What’s going on? That Fox is gonna be showing this science show with Neil deGrasse – I love it. I’m super excited.
    Female Speaker: This episode of Astronomy Cast is brought to you by 8th Light Inc. 8th Light is an agile software development company. They craft beautiful applications that are durable and reliable. 8th Light provides disciplined software leadership on demand and shares its expertise to make your project better. For more information, visit them online at www.8thlight.com. Just remember, that’s www. the digit 8, T H L I G H T.com. Drop them a note. 8th Light. Software is their craft.
    Fraser Cain: So put that pedal to the medal and accelerate. It’s not just velocity but the change in velocity. Let’s take a look at acceleration, how you measure it, and how Einstein changed our understanding of this exciting activity. So Pamela, am I accelerating right now?
    Pamela Gay: Yes.
    Fraser Cain: Really?
    Pamela Gay: Yes.
    Fraser Cain: How?
    Pamela Gay: You’re on a planet that is rotating and so your motion is constantly changing its direction. Our planet is also orbiting the sun so your motion is constantly changing direction and I’m fairly certain that since our planet’s motion around the sun is an ellipse rather than a perfect circle that even your speed relative to our motion along the orbit is varying. So you have both variations in speed and variations in direction and if you change either one of those aspects, you have an acceleration.
    Fraser Cain: Cool. Okay. So then I guess we’re gonna have to go into my – let’s start with, I guess, my physics, my high school physics version of acceleration before we move into my university physics version of acceleration. So what is acceleration?
    Pamela Gay: Acceleration is a change in velocity and velocity is speed in a direction. So if you change something’s speed, how fast it’s moving relative to the surroundings, regardless of direction, or if you change the direction that it’s moving in your X, Y, Z three dimensional reality, change either one of those factors and you have a velocity.
    Fraser Cain: Have an acceleration?
    Pamela Gay: Not a velocity. You have an acceleration.
    Fraser Cain: And as you sort of mentioned at the beginning of the show there, that your acceleration, it’s not just like I’m sitting in the car and I put the gas down and I can feel myself pushing back into the seat as I move. If I’m just going a constant velocity and I turn around a corner really quickly, I’m gonna feel an acceleration.
    Pamela Gay: And so there, you have to be careful because it wasn’t actually a constant velocity. It was a constant speed. Velocity is what’s called a vector property. Vectors are things that have a magnitude. So they have a number saying how much they are and they also have a direction. So velocity is a vector component because it has a direction that it’s going in and then it has a rate, a amount of distance over time that it’s going. So it’s that combination of DXDT and the little vector hadit letter of what direction you’re moving in.
    Fraser Cain: Right. And woe to the science writer who gets those two mixed up and writes it down and has to read the comments and apologize profusely. Not that that’s ever happened to me.
    Pamela Gay: No, never. Never at all.
    Fraser Cain: Right. So, right. Okay. So we got this situation, as you said, where I guess your speed doesn’t change but your velocity changes. Wait a second. Anyway, as you move around the corner, you are getting that acceleration in a sideways direction because you’re getting that change in velocity.
    Pamela Gay: And here’s where it starts to get really confusing because as your car goes around that corner, you feel yourself getting slammed outwards into the outer edge of the turn. So if I’m turning in this direction, I feel like my body’s getting forced out but the reality is the force is pointed inwards. That’s why I move in that direction. And me getting flung against the door is because my body wants to keep going straight and the car has moved around me and so it’s my failure to move conveniently with the car that creates this fictitional nonexistent force that makes it seem like I’m slamming into the door. The reality is the car moved; I have to catch up.
    Fraser Cain: And this is where we go down another rabbit hole and talk about the difference between centripetal and centrifugal force but we’ve done a whole show on that and I feel like we got that perfectly squared away so I don’t think we need to even talk about it anymore.
    Pamela Gay: Okay.
    Fraser Cain: Right. Okay. So this is my, what, my Newtonian comprehension of acceleration and then we’re presented with these various formulae to calculate, “If I jump off a cliff, how long does it take me to hit the water? If I throw a ball up into the air, how long does it take for the ball to come back down?” et cetera.
    Pamela Gay: So what is the one thing that’s always required in order to get an acceleration?
    Fraser Cain: Force.
    Pamela Gay: Force. Force equals MA. Force equals mass times acceleration. It is the one most important formula in all of physics. F equals MA.
    Fraser Cain: And that was one of the things, I guess, in high school physics where I was quite intrigued was just this concept of being in perfect balanced force that I am standing on the ground and I’m pushing down the ground and the ground is pushing back. And if I didn’t have that, then I would have acceleration.
    Pamela Gay: Right. And so people always talk about their feet hurt because gravity’s pulling them into the ground but they can also turn that around and say their feet hurt because gravity’s pulling the Earth into their feet. Both are valid.
    Fraser Cain: And think about the Earth. Think how sore the Earth is from all these feet –
    Pamela Gay: The surface.
    Fraser Cain: Yeah, getting pushed into it. It’s not fair.
    Pamela Gay: What? 6 billion feet?
    Fraser Cain: Yeah. Right? So okay. Yeah, and so that situation. So if you’re not moving, then the forces on your body are in perfect balance.
    Pamela Gay: Right. Now, the catch is this is where you start getting into frames of reference.
    Fraser Cain: Whoa. We just moved into the university physics, didn’t we?
    Pamela Gay: Yeah. It happens. Sorry.
    Fraser Cain: Okay. Alright. Well, it’s okay. We can cross that bridge now. Let’s go there.
    Pamela Gay: Okay. So here I am. I’m in a room in Portugal. The sun has now set. It’s no longer pretty outside and I feel like, except when I decide to rotate in the chair, I feel like I’m perfectly stationary but I’m not. I’m on a rotating, orbiting planet that’s in a solar system that’s whipping around the milky way which is on its way to fall towards the Virgo cluster while it’s also falling towards andro – there’s all these motions going on and I’m part of all of them. But from my perspective, I’m in an inertial frame of reference where everything seems to be balanced out and I can only measure things relative to my frame of reference. Kinda sucks.
    Fraser Cain: Right. So now is my frame of reference pretty much the same as your frame of reference right now?
    Pamela Gay: No. Because you and I are in different North South positions on the planet Earth, we’re different distances from the center of the planet. So while you feel like you’re experiencing nothing and I feel like I’m experiencing nothing, we are actually whipping around the center of the planet at two different velocities and because we’re different distances from the center of the planet, very miniscule because we’re both pretty darn close to sea level right now, but because we’re different distances from the center of the planet, we also are experiencing different gravitational pulls from the planet.
    Fraser Cain: Right. The acceleration of gravity from the planet. Right. Okay. But if I was on Mars, then I would see your acceleration different, right?
    Pamela Gay: If you were on Mars, we’d see our motion relative to one another and so it becomes the problem of we’re on planets that are both going around the sun but they’re going around the sun with the Earth moving faster than Mars and I can’t do that and keep my fingers on camera.
    Fraser Cain: Nice.
    Pamela Gay: So we’re on two planets that are orbiting the sun at different rates, at different distances, and so we do see motion relative to one another. You and I don’t actually see motion relative to one another unless we start looking at plate tectonics and that requires a whole lot of waiting I don’t feel like doing.
    Fraser Cain: Right. But I guess what’s very interesting about this is that as I’m on Mars and I watch you on Earth picking up speed and coming towards me, I’m seeing you accelerate. But from your perspective on Earth, you’re not feeling that acceleration even though it’s happening.
    Pamela Gay: And this is where one of the things that Einstein came up with was the realization that no two observers ever observe the exact same thing. You and I are both experiencing the passage of time every so slightly different. If you put us on two different worlds, we see one another’s motion as different if we each assume that we are stationary and the other one is moving.
    And so when it comes to trying to sort out simply the time of when something took place, no two observers will necessarily see the exact same time without doing all sorts of mental and computational arithmetic to sort out the differences in time generated due to relativistic effects and just light travel time. If you and I both observe, and I don’t know if we can because I think we’re actually 180 degrees apart right now – no, we’re both on –
    Fraser Cain: We’re eight hours. We’re eight hours apart. Right? So we’re –
    Pamela Gay: We’re eight hours so we’re fine. Yeah. So you and I can –
    Fraser Cain: We’re a third of an Earth away from each other.
    Pamela Gay: You and I can both observe the moon at the same time once it gets much higher in the sky and so if we both were able to observe a meteor crashing into the edge of the moon and letting out a fireball to the side – this isn’t going to happen tonight. I’m just saying a what if. If you and I both observed that same what if, because the distance from me to the moon and from you to the moon is different, we’re going to end up seeing different timings for that event and then when you take into consideration the amount of time that it takes a signal to reach from me to you and you to me, there’s whole lot of things that have to be taken into consideration. So you and I might both say, “Hey, I saw it,” but we didn’t see it at the same time.
    Fraser Cain: Right. Now, so what was sort of this big change, the university level physics, the college level physics that Einstein had sort of come up with, right, about his sort of fundamental understanding of what acceleration is?
    Pamela Gay: Well, so prior to that, we started to get from Galileo ­– because you do have to step back a little bit further. From Galileo, we’d gotten the idea that an object in motions tends to stay in motion and an object at rest tends to stay at rest.
    Fraser Cain: Newton?
    Pamela Gay: No, Galileo actually.
    Fraser Cain: Galileo. Okay.
    Pamela Gay: Yeah, yeah. So we have to step back to Galileo. So when you step back to Galileo, you get an object in motion stays in motion, and object at rest stays at rest. It as Galileo who figured out the concept of friction. Prior to that, it was an object in motion would come to rest but then how do you explain the moon? How do you explain the stars? And Galileo was not pleased with the explanation of, “That’s just the way it is. They’re heavenly bodies.”
    He wanted more reality and he figured out friction. He figured out inclined planes and that there’s a similar amount of acceleration if something falls straight down or if it goes down all the way down to the bottom of an incline. You’re changing the same amount of potential energy into kinetic energy no matter what route you take.
    And so Galileo put all of these initial ideas together but beyond sorting out friction, he didn’t get the underlying concepts of you need to put the same amount of force on a two different objects if they have the same mass and you want the same acceleration. So this is if you have a pound of feathers and you have a pound of lead, they’re both going to fall at the same time, ignoring aerodynamics. The concept of mass, gravitational acceleration equals a force. That came from Einstein.
    The next thing that came – not Einstein. Came from Newton, Isaac Newton. The next thing that came from Isaac Newton was the concept that the moon is actually falling around the earth, that it’s a force that keeps it in place. This was very mysterious. We had Kepler’s laws explaining the motions along ellipses. We had Galileo trying very hard to get at the concept of forces and then we had to wait for Isaac Newton to get born and grow up and develop calculus and figure out that the moon is actually falling but as it falls, it’s able to miss the planet Earth but it’s constantly falling in an ellipse as it goes around and he was able to work out and balance all the forces.
    Fraser Cain: And thanks Galileo. Have you ever done that experiment where you roll a bunch of cylinders?
    Pamela Gay: Oh, I have not only done that experiment. I have forced students to do that experiment with water clocks like the one Galileo used.
    Fraser Cain: Oh, really?
    Pamela Gay: Yeah. Yeah.
    Fraser Cain: And I guess that’s the whole point. Right? Is that the timing is terrible so you wanna slow down that whole process to use the inclined plane to kind of slow the whole system down.
    Pamela Gay: You can actually get surprisingly accurate with a water clock and everything gets measured in milliliters of water instead of in seconds of time.
    Fraser Cain: What’s your favorite experiment to do? Is that the one with the inclined plane to sort of demonstrate acceleration and gravity and things like that?
    Pamela Gay: I don’t know if that one’s my favorite. I think my most satisfying one is actually a pendulum experiment where you suspend a ball bearing in a sling of saran wrap, pull it back and release it so that the saran wrap gets cut by a hot wire and then the ball will go flying off and you can calculate exactly where it should land. And when I do this with students, I give them just a soup can and I say, “Okay, run the calculations. Put the soup can where you think the ball bearing’s gonna land,” and they’re always shocked and amazed when it actually works.
    Fraser Cain: That’s really cool.
    Pamela Gay: It’s highly satisfying. Physics at work with a thunk.
    Fraser Cain: Right. And it landing sort of where their math predicted it would land which is really neat. Yeah. So I guess the thing is that it’s kind of mind bending. When we go back to sort of the Einstein concept of acceleration, when you think about that frame of reference, in the classical understanding, these things are all true that you’re dropping this cylinder and it’s rolling down a slope and it’s landing at the bottom, but Einstein, I think, really kind of turned that all on its ear with his concept of these frames of reference in the fact that it’s all relative that from your perspective, maybe, but there are other perspectives out there that aren’t seeing what you’re seeing.
    Pamela Gay: But the one neat thing that came out of it was things like the twin paradox and the twin paradox gets defined by who’s the poor saud that’s getting accelerated through space. So the concept here, and we’ve discussed this in depth in other shows, is the speed of light remains constant for all observers. So if you’re moving, in order for you to perceive the speed of light of the flashlight you’re holding in your hand as a constant, time has to slow down for you so that you aren’t catching up to the waves and seeing lights slow down.
    So if you have two observers and one stays on the planet Earth and the other one accelerates away from the planet Earth at high enough rates that time perceivably slows down, it’s the one that does that accelerating that experiences the slow down of time and the slow down of age and eventually gets called Buck Rogers.
    Fraser Cain: Right. That’s it. They always have to change the name to Buck Rogers.
    Pamela Gay: Always. Yes.
    Fraser Cain: Yeah. Yeah. I loved that show. Right. And the twin paradox, there was really interesting – I’m trying to remember what it was. I see so much of this stuff. But someone had just sort just done the math about if you did wanna go and travel across the universe, essentially, and if you could get yourself going fast enough that you could almost survive. In a human lifespan, for you to be like, whatever, in 100 years, you could pretty much get completely across the universe if you were going fast enough from your perspective and yet billions and billions of years would have happened for the rest of the universe.
    Pamela Gay: It’s actually quite useful because there’s particles called muons that are highly unstable and reformed when high energy particles hit our atmosphere. And because they’re moving very fast, they’re able to make it all the way to the surface of the planet to get detected in what, to them, is a fraction of a second but is a perceivable amount of time to us poor sauds on the surface of the planet.
    Fraser Cain: Now, what is it called where if the acceleration is changing? You know that?
    Pamela Gay: It’s called a change in acceleration.
    Fraser Cain: So there isn’t a whole set –
    Pamela Gay: It’s the first derivative of acceleration, which –
    Fraser Cain: Right. Yeah.
    Pamela Gay: So all of these are derivatives in calculus. So the way to think of it is you have a position. Your change in position over your change in time is your velocity. Your change in position per second per second. So in per unit time, so every distance I go increases ever interval of time. That’s my acceleration. If I take another derivative of that, that’s when I start to get the change in the rate of acceleration, which is another derivative.
    Fraser Cain: Now, I wanna do a little mind experience with you here. Let’s imagine that you were inside an elevator. You’re like ten stories up and you’re going down and then the rope breaks and you fall to the ground and then just before you hit the ground, you jump up and you avoid certain death.
    Pamela Gay: No.
    Fraser Cain: Now, am I fundamentally misunderstanding acceleration here? What’s going on? Because I think people think this is the case and obviously it’s not the case. So what’s wrong with that thought experiment?
    Pamela Gay: As the elevator falls, you are now in a weightless environment where you and the elevator are both moving relative to gravity in free fall. And so first of all, you can’t really jump up because you’re kinda hovering in the middle of the elevator quite likely and it’s one of those horrible situations where first you get slammed into the top of the elevator and then you’re in free fall and then you die at the bottom with the sudden deceleration which, again, slams you into the ceiling of the elevator.
    Fraser Cain: Right. So I guess the point being that you’re in free fall. You and the elevator are falling at the same speed. You are still falling that entire distance.
    Pamela Gay: Yeah. And the elevator hits the ground first and begins its deceleration first, causing you to decelerate against it.
    Fraser Cain: Right. So you would – well, I guess you would smash into the ground second or milliseconds after the elevator starts its smashing into the ground. Yeah. And unless the top of the elevator could pop open and you could –
    Pamela Gay: Yeah, but then you still have all of that potential energy to convert into crashing energy.
    Fraser Cain: Right. No and you could jump the height of the building –
    Pamela Gay: Yeah. No. You’re just making stuff up now.
    Fraser Cain: And you could somehow get yourself down to the bottom of the elevator. If you could pull off those things, then you’d be safe.
    Pamela Gay: No. No. So the whole problem is when you’re ten stories up, you have a certain amount of gravitational energy, gravitational potential energy. As you fall, all of that gets turned into kinetic energy. Under normal circumstances, the elevator transforms that potential energy into friction and other things that the elevator’s absorbing, generating in the form of heat, sound, other stuff into the environment around it. Remove that dissipation of energy.
    As you fall, all your gravitational potential energy becomes kinetic energy. That kinetic energy has to get dissipated somehow when you and the elevator hit the ground and it’s gonna end up turning into sound, deformation of the elevator, defamation of you. Generally, things you don’t wanna experience.
    Fraser Cain: Right. Right. It would be a very bad day.
    Pamela Gay: Yeah, it’ conservation of energy. It’s a problem.
    Fraser Cain: Alright. Well, so hopefully people can kinda take that back – actually, Myth Busters did a great experiment on it. They actually tried to test it and demonstrated that yes, it’s ridiculous and you’re not gonna help yourself at all so.
    Pamela Gay: Death.
    Fraser Cain: Death. Death. Death. All you get is death.
    Pamela Gay: Okay.
    Fraser Cain: Okay, great. Well, thank you very much, Pamela.
    Pamela Gay: My pleasure.
    Male Speaker: Thanks for listening to Astronomy Cast, a non profit resource provided by Astrosphere New Media Association, Fraser Cain, and Dr. Pamela Gay. You can find show notes and transcripts for every episode at AstronomyCast.com. You can email us at info@astronomycast.com. Tweet us @astronomycast. Like us on Facebook or circle us on Google+. We record our show live on Google+ every Monday at 12:00p.m. Pacific, 3:00p.m. Eastern or 2000 Greenwich Mean Time. If you miss the live event, you can always catch up over at CosmoQuest.org.
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    [End of Audio]
    Duration: 27 minutes

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