Mechanical Energy- Geosynchronous Orbit

AI Thread Summary
To calculate the total mechanical energy of a 290 kg satellite in a geosynchronous orbit, the relevant equations include kinetic energy (K) and gravitational potential energy (UG). The satellite's orbital period is equal to the Earth's rotation period, which is 24 hours, allowing for the determination of the orbital radius. The gravitational force provides the necessary centripetal force, leading to the relationship between orbital speed and radius. Solving for initial speed first can simplify finding the radius. Understanding the geosynchronous nature of the orbit is crucial for accurate calculations.
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Homework Statement


What is the total mechanical energy of a 290 kg satellite in a geosynchronous orbit around the Earth?


Homework Equations


W= K + UG where K= 1/2 (mv2) and UG= -(GmM)/r
Fc= mac where ac= v2/r


The Attempt at a Solution


I think the geosynchronous part is what is throwing me off. What would the radius be so I can solve for the initial speed.
 
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I don't want to throw you off, but I think it might be easier to find the initial speed first then find the radius. It's a geosynchronous orbit, so what do you know about its period?
 
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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