Physics problem

[Ian]

I have a physics equation that needs-a-figurin'.

How much g-force is created by accelerating an object (assuming the mass of the object is not relevant) from 0 to 86.6% the speed of light in exactly 30 minutes? Assuming constant acceleration in between the start and end of acceleration, of course; no need to over-complicate this.

I think I have an answer, but it's been quite a few years since I did physics equations so I don't trust my brain on this.

[Rum]

I can't begin to answer this but it would be a massive G force - several million Gs equivalent over such a short time I would guess! I am intrigued though - why 0.886%?

[Ian]

I can't begin to answer this but it would be a massive G force - several million Gs equivalent over such a short time I would guess! I am intrigued though - why 0.866%?

Sort of random - that's the speed that results in a Lorentz factor of 2.0 - time onboard a spacecraft travelling at that speed passes by twice as slowly as real-time. If I left on Monday at noon on this ship and stopped back at Earth on Wednesday at noon, I'd feel like only 24 hours had passed instead of 48. Lorentz factors go up exponentially as one approaches lightspeed, though (theoretically) the time dilution would go up to almost infinity since lightspeed itself cannot be broken by normal matter (theoretical propulsion drives excepted, of course).

There's an interesting (old) sci-fi book on this called Tau Zero. A spaceship's engine gets stuck in "accelerate" mode and cannot be decelerated, and eventually the crew start experiencing millions of years' worth of travel in a matter of seconds as they slowly approach lightspeed.

[Thinking Aloud]

144233.48 ms-1, which is 14717g.

[Ian]

144233.48 ms-1, which is 14717g.

14,717g? It can't be that low. The electronics inside modern artillery shells are rated at 15,500g.

I figured about 860,000g for thirty minutes to get to that speed.

[Rum]

There be some clever sods on this here forum and thats a fact!

[colubridae]

I have a physics equation that needs-a-figurin'.

How much g-force is created by accelerating an object (assuming the mass of the object is not relevant) from 0 to 0.866% the speed of light in exactly 30 minutes? Assuming constant acceleration in between the start and end of acceleration, of course; no need to over-complicate this.

I think I have an answer, but it's been quite a few years since I did physics equations so I don't trust my brain on this.

I'm not sure what you mean by g-force.

g-force is a 'construct' used to denote the amount of force applied to a given mass to give it an acceleration equal to that of the local value of the acceleration of gravity at the surface of the earth.
As I defined it above it would depend on the mass of the object being accelerated.

also if you are talking about the force required to exactly accelerate the mass to 0.886 c in 30 minutes then (assuming you want a constant force for the 30 minutes) you may find it easier to use an energy divided by time type equation, otherwise the calculation will need calculus (it might need it anyway). As the mass accelerates it gains mass and its acceleration will decrease as the mass increases for a constant force.

If however you mean g-force as a simple acceleration then it’s just 0.886c/30 mins.

Not sure i've been clear. hope it helps

[Ian]

I'm looking for the simplest possible answer: If I were onboard a ship that accelerated to that speed over that period of time, how much gravity would I feel from the thrust?

(Enough to turn me into fine guacamole no doubt, but that's beside the point)

[Magicziggy]

V = u+ at

Where v = final velocity = 0.866c
U= initial velocity
a= acceleration
t = 30x 60 seconds. = 1800

Assuming u = 0
c= 299,792,458 m/s

a = 0.866c / 1800
a = 1442142 m/s

I may be off beam with this

[Ian]

Thanks for the PM colubridae. Maybe it really is around 14,700g.

Well done also, TA.

[Kr]

I'm confused.

Doesn't 0.866% of the speed of light equal 0.00866c?

Edit: Looked up Lorentz factor. Guess you just didn't need that % on the end there.

[Ian]

Kr pointed something out - I think I messed up the OP by saying 0.866%. What I meant was 86.6% of lightspeed, or 0.866c.

[JimC]

Assuming you meant 0.866%, not 86.6%, my answer was 147 g

[Ian]

Assuming you meant 0.866%, not 86.6%, my answer was 147 g

14,700g it is then. Thanks everybody.

Not nearly as much as I first calculated (because I guess I'm a physics rube). This makes things easier for the sci-fi novel I'm writing. If modern electronics can be rated at withstanding over 15,000g, then surely graphene can take that amount of force.

[JimC]

Assuming you meant 0.866%, not 86.6%, my answer was 147 g

14,700g it is then. Thanks everybody.

Not nearly as much as I first calculated (because I guess I'm physics rube). This makes things easier for the sci-fi novel I'm writing. If modern electronics can be rated at withstanding over 15,000g, then surely graphene can take that amount of force.

Yep, I recalculated, and 14,744 g it is...

However, the real figure would be somewhat higher. As you approach the speed of light, the Lorenzt equations come in to play. The velocity graph is no longer linear, but its gradient starts to decrease, with c being its eventual asymptote. In effect, at these higher speeds, a steadily increasing proportion of the energy you supply ends up as a mass increase, rather than a velocity increase.

Given time, I should be able to dig out the equations, and work out what the "somewhat higher" would be; I dont think it would be more than a few % higher at 87% c...