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Making high school physics problems more fun

Making high school physics problems more fun

(OP)
I'm trying to inject some fun ideas into the seemingly dry topic of high school physics for my son (gravity, mass, acceleration, Newton's laws).
The old questions with inclined planes, balls swung on strings, and cars on frictionless curved roads have been done to death and I'm thinking up some more interesting ones (without making them too hard for a teenager).
If you know of other interesting types of problems that we can work on together, please let me know.
I am also working on a problem inspired by a sci-fi short story I once read, about a stunt man who jumped off a cliff on Miranda with a pellet gun to slow his fall.

(1)
An astronaut lands her spacecraft on a rocky asteroid that is 50 km across that rotates once per (earth) day. The astronaut (carefully!) walks all the way around the asteroid to explore, before getting back in her spacecraft and landing on another asteroid. The second asteroid is also 50 km across, and it spins once per hour. The astronaut lands at the pole of this asteroid, and before landing, notices that it is also rocky and very spherical. Can the astronaut walk all the way around this asteroid?
To help you solve this problem, the density of rocky asteroids is about 2000 kg per cubic meter, and the volume of a sphere is 4/3*pi*Rad^3.

(2)
If the Earth turned once per hour, instead of once per day, what would happen?


NB, considering Eng-Tips rules about posting homework problems, please don't red-flag me!

For those who care to check the math (or who dare to believe I could get it wrong!)

Spoiler:


M = rho * 4 / 3 * pi * rad ^3 = 1.1 E21 kg
g = G * M / Rad^2 = 0.029 m/sec^2
Vt = w * Rad = 87 m/sec
a = Vt^2 / Rad = 0.15 m/sec^2

So the answer is "No she can't walk around without being thrown off the surface"

The answer to (2) is similar and EVERYTHING would be thrown off into space if the Earth turned that fast!

The problem ignores, of course, the inability for this asteroid to even form with that much angular momentum - but astronomy and planetary physics are next year...

STF

RE: Making high school physics problems more fun

(OP)
Yeah, and just walking on the surface flirts with the escape velocity even at the pole...

STF

RE: Making high school physics problems more fun

Diffferent versions of MathCAD? and, what happens once she's up to speed <G>?

Dik

RE: Making high school physics problems more fun

(OP)
My own hand calcs had the Radius at 50 km, but my verbal text called it the diameter. Sorry IRStuff!

I also started punching these equations into Mathcad. Got some strange answers until I realized there is an environment variable setting the exponential threshold. Mine was set at ^15. Moved it to ^50 and suddenly it made sense again.

I haven't shown my son MathCAD yet. Not sure it would be a good idea to do so while he is still learning to handle units in equations etc.

STF

RE: Making high school physics problems more fun

I got IR's mass with excel. I figure you used 500,000m (that's what I needed to get 1E21).

As others have pointed out if walking is impossible, how about landing. ok, the lander would synchronize with the surface, but the lander legs would still have to transfer a bunch of shear, no? (the same that the astronaut feels) maybe the legs have very strong harpoons, embedded into the surface ? why not have the same on the astronaut's boots ? what if the astronaut had a little thruster that countered the inertial force ??

nice "her" !

another day in paradise, or is paradise one day closer ?

RE: Making high school physics problems more fun

I get that the surface velocity is something like 43m/sec, and the inertial acceleration (w^2*R) is 0.027m/sec^2.

That tells me that the astronaut might get dizzy (watching the universe wiz by) but she wouldn't feel the surface velocity as it's within her frame of reference. And the force she'd be exposed to doesn't look to be untenable ?

but what would happen to small stones etc that she might kick up as she walks ? would they "instantly" decelerate ?

another day in paradise, or is paradise one day closer ?

RE: Making high school physics problems more fun

(OP)
Hi RB,
That's where the "thought experiment" gets a little wild. If she can't stand on the surface, due to excessive rotation, then pebbles, dust, rocks too would also have been flung off long ago.
Given the structural integrity of a typical asteroid (if comets Halley and the unpronounceable Russian are similar enough to be a guide) the mishmash of rock and ice would split apart at the first stray impact.
Which then leads us to ask: How could such an asteroid even form? Answer is: it couldn't. Accretion is impossible because the angular momentum it too high, and a glancing impact that spins up the asteroid to 1 rev/hour would also have the energy to shatter it.

This thought experiment is something I took an interest in because, long ago, I wrote a school paper about hollowing out asteroids and spinning them up for artificial gravity.

Walking on the surface of asteroids, spinning or not, is a dicey thing. Even the Apollo astronauts had to be careful with the moon's low gravity. They could easily have taken an energetic stride high in the air, but without control of the liftoff they could find themselves flipped upside down by the time they returned to the ground, several seconds later. Those backpacks didn't help.

STF

RE: Making high school physics problems more fun

"would they "instantly" decelerate"

no, assuming the rock was somehow attached to the surface and the astronaut broke it free, it would simply go in a straight line tangential to where it broke off at the surface's speed until it hit something.


"How could such an asteroid even form? Answer is: it couldn't"

There are asteroids that were ejecta from collisions with Moon and other planets, so I'm not sure that such an asteroid couldn't exist.

I think you gilded the lily a bit; anything shorter than a 140.05-minute day would make it challenging

TTFN (ta ta for now)
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