How Fast Must an Astronaut Run in Skylab to Mimic Earth's Gravity?

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To mimic Earth's gravity while running in Skylab, an astronaut must achieve a speed that creates centripetal acceleration equivalent to Earth's gravitational acceleration (g). The formula used is v = sqrt(gr), where 'r' is the radius of the circular path. An estimated radius of about 3 meters was suggested for the calculations. The discussion highlights the importance of using the correct terminology, noting that it should be centripetal acceleration rather than centrifugal. Understanding these principles is crucial for accurately setting up the problem.
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Homework Statement



The attached videoclip shows footage from Skylab, launched in 1973, used during 1973-74, and in orbit until 1979. During the final seconds of the clip, you can see three astronauts exercising. One of them is running around the station. Estimate the speed that he should maintain, in order to feel as if he were running on earth...explain your reasoning and calculations


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The Attempt at a Solution



idk, I'm really looking for how to set the problem up more than estimates. I tried this...really no idea if its right or not.

centrifugal acceleration = v^2 / r

= g (to feel like you are on earth)

So v = sqrt (gr)

and estimated radisu to be about 3m
 
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That looks right to me. The only thing wrong is your wording. It is centripetal acceleration not centrifugal.
 
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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}...
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