Forming Proper Equation to Calculate Speed of Spaceship

  • Thread starter Thread starter ND3G
  • Start date Start date
  • Tags Tags
    Length
AI Thread Summary
To determine the speed at which a spaceship's relative length is half its proper length, the equation L = (Lo)(sqrt(1 - (v^2)/(c^2))) is used, where Lo is the proper length and L is the observed length. Given a proper length of 67m and a relative length of 33.5m, the calculation for speed v involves rearranging the equation to v = sqrt((1 - (L/Lo)^2)(c^2)). The initial calculation yielded a non-real answer due to an arithmetic error in dividing Lo by L. Correcting this reveals that the proper approach leads to a valid solution for the speed required.
ND3G
Messages
79
Reaction score
0
"proper" Length

What speed would the spaceship have to travel for its relative length to be half its “proper” length

Given:
Lo = 67m
L = 33.5

Required:
v

Analysis:
L = (Lo)(sqr(1-(v^2)/(c^2)))

Now, I calculate v = sqr((1-(L/Lo)^2)(c^2)) however that gives me an non-real anwer. Clearly my algebra is lacking somewhere.

Can anyone help me form a proper equation for this?
 
Physics news on Phys.org
Your algebra looks fine. Your arithmetic seems to be lacking. L/Lo=1/2, 1-(1/2)^2=3/4 etc etc.
 
Ah, yes, I was dividing Lo/L on paper. It is always the simplest things...

Thanks
 
Thread 'Variable mass system : water sprayed into a moving container'

Thread 'Variable mass system : water sprayed into a moving container'

Starting with the mass considerations #m(t)# is mass of water #M_{c}# mass of container and #M(t)# mass of total system $$M(t) = M_{C} + m(t)$$ $$\Rightarrow \frac{dM(t)}{dt} = \frac{dm(t)}{dt}$$ $$P_i = Mv + u \, dm$$ $$P_f = (M + dm)(v + dv)$$ $$\Delta P = M \, dv + (v - u) \, dm$$ $$F = \frac{dP}{dt} = M \frac{dv}{dt} + (v - u) \frac{dm}{dt}$$ $$F = u \frac{dm}{dt} = \rho A u^2$$ from conservation of momentum , the cannon recoils with the same force which it applies. $$\quad \frac{dm}{dt}...
View full post »

Thread 'Egg Drop Challenge! Need ideas for winning designs'

I was thinking using 2 purple mattress samples, and taping them together, I do want other ideas though, the main guidelines are; Must have a volume LESS than 1600 cubic centimeters, and CAN'T exceed 25 cm in ANY direction. Must be LESS than 1 kg. NO parachutes. NO glue or Tape can touch the egg. MUST be able to take egg out in less than 1 minute. Grade A large eggs will be used.
View full post »

Similar threads

What is the length of an electron's journey in its own frame of reference?
Replies
2
Views
1K
Length Contraction of spaceships
Replies
2
Views
2K
Calculating the Planck Length
Replies
3
Views
261
Length Contraction Formula: How to Calculate Observed Length at High Speeds
Replies
9
Views
3K
Relativistic mass/length contraction problem
Replies
3
Views
2K
Special relativity (length contraction, velocity composition) problem
Replies
2
Views
1K
Length Contraction & Time Dilation
Replies
5
Views
2K
Solving Simple SR Questions: Find Proper Length & Speed of a Spacecraft
Replies
6
Views
1K
How Does Relativistic Speed Affect Spaceship Length?
Replies
3
Views
3K
Special Relativity Spaceship Question
Replies
3
Views
2K

Hot Threads

Recent Insights

Back
Top