Physics problem
 

If you traveled to Pluto accelerating at 1 gravitational pull and then at the halfway point started deccelerating at 1 gravitational pull would you ever approach the speed of light?

Yes, the moment you accelerate you're approaching the speed of light.



You're still quite far from it, but you're approaching it :D


How close do you want to be to the speed of light? 1%? 10%? 95%?

yes but it would hurt like a sonofabooch...

if you put a straw from earth to outer space, will it suck out all the oxygen?

The answer is no, you're no where near the speed of light.

g accel (approx)= 10m/s/s; c= 300,000,000m/s. It would take 30,000,000 seconds to reach the speed of light, or about 347 days.

Pluto ranges from 4,400,000,000,000m to 7,300,000,000,000m from us, so lets say 6,000billion meters avg., so we would have 3,000 billion meters in which to accelerate before we had to begin to shut down. Or 30 million seconds, whichever comes first.

It's been way too long since I did algebra and calculus, but we need now to figure out how long it would take to reach 3,000 billion meters at a constant acceleration of 10m/s/s. If it is less than 30 million seconds you have achieved warp speed.

I think.

Easy peasy...

Half distance to Pluto = 20AU= 2991960000000m
1g ~ 10m/sec^2

If we use speed/distance/acceleration formula and start with 0 speed...
http://upload.wikimedia.org/math/6/d...0196d8219a.png

...it boils down to 0.02c for 1g across 20AU. (v=27848088km/h. Speed of light is 1080000000km/h) . Not even enough to experience relativistic effects.


Can I get my friday beer now? :D

You have two equations that must be be solved:
d=1/2 a * t^2
v=a * t

Take the first one:
d=3,670,052,070 miles total, we want half of that, or 1,835,026,035 miles
a=32 ft/sec^2 which is 0.00606 mile/sec^2
From that, you can get the travel time to the halfway point at constant acceleration of G.

Then, you use the same value for "a" and the derived value for "t" to solve for "v", which will be your velocity at that point.

The distance measurements are the average Sun/Pluto distance. If you want the actual Earth/Pluto distance, you have to state a date, since they vary between 38.5 and 40.5 AU.

I had to look it up... it was driving me crazy. d= .5 *g * t^2 (like Mike says)

The distance we are allowed to accelerate is roughly 6,000 billion meters. .5g = 5m/s/s
Therefore t^2 = 1200 billion sec^2, square root = 1,095,445 secs.

Thus, it would take approx. 1.1 million secs to travel 1/2 way to Pluto at a constant g acceleration. 1.1 million seconds at 10m/s/s = terminal velocity of 11million m/s... far below the speed of light at 300million m/s.
(Remember earlier that we had calculated that it would take approx 30 million secs to reach the speed of light at g accel. We ran out of dragstrip here before we had to shutdown)

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Corect answer... 3.66%. Your first guess was pretty good!

Everyone has forgotten a basic. The starting point is not at zero. We are moving thru space as a system, and here on Earth, some additional orbital mechanics are invovled. What would be the real starting point? Relatively and relativity speaking?

Pluto's orbit is also slightly inclined (relative) to ours as I remember. Does this affect the flight path and accel?

Makes the healthcare debate seem trivial doesn't it. One commonality tho.

Lots of zeros in both answers.

Damn I gave you guys an hour and ya already got it. Cool. So now I can write all that out and go get the bonus from my calc teacher. He said he didn't care how we came up with it even if it involved buying someone a 12 pack.

fingpilot... I think theassumption is that you'd travel point A to B in a straight line, and initial velocity from earth would be zero.

Calcuating gravity effects and orbital trajectories is not something you cover in high school physics.

Hey I am not High school. And this was a problem proposed for extra credit in my college calc class.

Tell your teacher there is no calculus involved, you want a harder problem please.

http://forums.pelicanparts.com/uploa...1253298206.jpg

Boobs... thats the answer...

The speeds you are getting to are relativistic. You can not solve this with classical mechanics. If the instruction is to solve this with classical mechanics, follow the path above. Otherwise you can answer this very quickly: You can not reach light speed in a space ship, as the relativistic mass increases with speed and your acceleration required to further increase velocity is going to be approaching infinity.

George

Why would you want to go to Pluto when you can go to Uranus?

Closer to 2.5% of C when you sit and crank the numbers.

Then where did that "1/2" come from in d=1/2at^2??? Calculus rears it's ugly head again!!

No where near relativistic. The Lorenz Factor at that velocity is 0.99679. Therefore, the velocity is in the order of that far off...about 1 mile per second off.