Seesaw to The Stars

I look around the playground. “Where’s the seesaw, Teena?”

“They took it away. That’s good ’cause I hated that thing!”

“Why’s that, Sweetie?”

“I never could play right on it. Almost never. Sometimes there’d be a kid my size on the other end and that worked OK, but a lot of times a big kid got on the other end and bounced me up in the air. The first time I even fell off and they laughed.”

“Well, I can understand that. I’m sure you’ve been nicer than that to the littler kids.”

“Uh-huh, except for Bratty Brian, but he liked it when I bounced him. He called it ‘going to the Moon’.”

“I can understand that, too. If things go just right you come off your seat and float like an astronaut for a moment. I bet he held onto the handles tight.”

“Yeah, I just wasn’t ready for it the first time.”

“Y’know, there’s another way that Brian’s bounces were like a rocket trip to somewhere. They went through the same phases of acceleration and deceleration.”

“Uncle Sy, you know you’re not allowed to use words like that around me without ‘splaining them.”

“Mmm, they both have to do with changing speed. Suppose you’re standing still. Your speed is zero, right? When you start moving your speed isn’t zero any more and we say you’ve accelerated. When you slow down again we say you’re decelerating. Make sense?”

“So when Bratty Brian gets on the low end of the seesaw he’s zero. When I squinch down at my end he accelerates –“

“Right, that’s like the boost phase of a rocket trip.”

“… And when he’s floating at the very top –“

“Like astronauts when they’re coasting, sort of but not really.”

“… And then they decelerate when they land. Bratty Brian did, too. I guess deceleration is like acceleration backwards. But why such fancy words?”

“No-one paid much attention to acceleration until Mr Newton did. He changed Physics forever when he said that all accelerations involve a force of some kind. That thought led him to the whole idea of gravity as a force. Ever since then, when physicists see something being accelerated they look for the force that caused it and then they look for what generated the force. That’s how we learned about electromagnetism and the forces that hold atoms together and even dark matter which is ultra-mysterious.”

“Ooo, I love mysteries! What did Mr Newton tell us about this one?”

“Nothing, directly, but his laws gave us a clue about what to look for. Tell me what forces were in play during Brian’s ‘moon flight’.”

“Let’s see. He accelerated up and then he accelerated down. I guess while he was on the seesaw seat at the beginning the up-acceleration came from an up-force from his end of the board. And the down-acceleration came from gravity’s force. But the gravity force is there all along, isn’t it?”

“Good point. What made the difference is that your initial force was greater than gravity’s so Brian went up. When your force stopped, gravity’s force was all that mattered so Brian came back down again.”

“So it’s like a tug-of-war, first I won then gravity won.”

“Exactly. Now how about the forces when you were on the merry-go-round?”

“OK. Gravity’s always there so it was pulling down on me. The merry-go-round was pushing up?”

“Absolutely. A lot of people think that’s weird, but whatever we stand on pushes up exactly as hard as gravity pulls us down. Otherwise we’d sink into the ground or fly off into space. What about other forces?”

“Oh, yeah, Mr Newton’s outward force pushed me off until … holding the handles made the inward force to keep me on!”

“Nice job! Now think about a galaxy, millions of stars orbiting around like on a merry-go-round. They feel an outward force like you did, and they feel an inward force from gravity so they all stay together instead of flying apart. But…”

“But?”

“Mr Newton’s rules tell us how much gravity the stars need to stay together. The astronomers tell us that there aren’t enough stars to make that much gravity. Dark matter supplies the extra.”

~~ Rich Olcott

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Gravity and other fictitious forces

In this post I wrote, “gravitational force is how we we perceive spatial curvature.”
Here’s another claim — “Gravity is like centrifugal force, because they’re both fictitious.”   Outrageous, right?  I mean, I can feel gravity pulling down on me now.  How can it be fictional?

Fictitious triangle
A fictitious triangle

“Fictitious,” not “fictional,” and there’s a difference.  “Fictional” doesn’t exist, but a fictitious force is one that, to put it non-technically, depends on how you look at it.

Newton started it, of course.  From our 21st Century perspective, it’s hard to recognize the ground-breaking impact of his equation F=a.  Actually, it’s less a discovery than a set of definitions.  Its only term that can be measured directly is a, the acceleration, which Newton defined as any change from rest or constant-speed straight-line motion.  For instance, car buffs know that if a vehicle covers a one-mile half-mile (see comments) track in 60 seconds from a standing start, then its final speed is 60 mph (“zero to sixty in sixty”).  Furthermore, we can calculate that it achieved a sustained acceleration of 1.47 ft/sec2.

Both F and m, force and mass, were essentially invented by Newton and they’re defined in terms of each other.  Short of counting atoms (which Newton didn’t know about), the only routes to measuring a mass boil down to

  • compare it to another mass (for instance, in a two-pan balance), or
  • quantify how its motion is influenced by a known amount of force.

Conversely, we evaluate a force by comparing it to a known force or by measuring its effect on a known mass.

Once the F=a. equation was on the table, whenever a physicist noticed an acceleration they were duty-bound to look for the corresponding force.  An arrow leaps from the bow?  Force stored as tension in the bowstring.  A lodestone deflects a compass needle?  Magnetic force.  Objects accelerate as they fall?  Newton identified that force, called it “gravity,” and showed how to calculate it and how to apply it to planets as well as apples.  It was Newton who pointed out that weight is a measure of gravity’s force on a given mass.

Incidentally, to this day the least accurately known physical constant is Newton’s G, the Universal Gravitational Constant in his equation F=G·m1·m2/r2.  We can “weigh” planets with respect to each other and to the Sun, but without an independently-determined accurate mass for some body in the Solar System we can only estimate G.  We’ll have a better value when we can see how much rocket fuel it takes to push an asteroid around.

CoasterBut there are other accelerations that aren’t so easily accounted for.  Ever ride in a car going around a curve and find yourself almost flung out of your seat?  This little guy wasn’t wearing his seat belt and look what happened.  The car accelerated because changing direction is an acceleration due to a lateral force.  But the guy followed Newton’s First Law and just kept going in a straight line.  Did he accelerate?

This is one of those “depends on how you look at it” cases.  From a frame of reference locked to the car (arrows), he was accelerated outwards by a centrifugal force that wasn’t countered by centripetal force from his seat belt.  However, from an earthbound frame of reference he flew in a straight line and experienced no force at all.

Side forceSuppose you’re investigating an object’s motion that appears to arise from a new force you’d like to dub “heterofugal.”  If you can find a different frame of reference (one not attached to the object) or otherwise explain the motion without invoking the “new force,” then heterofugalism is a fictitious force.

Centrifugal and centripetal forces are fictitious.  The  “force” “accelerating” one plane towards another as they both fly to the North Pole in this tale is actually geometrical and thus also fictitious   So is gravity.

In this post you’ll find a demonstration of gravity’s effect on the space around it.  Just as a sphere’s meridians give the effect of a fictitious lateral force as they draw together near its poles, the compressive curvature of space near a mass gives the effect of a force drawing other masses inward.

~~ Rich Olcott