Gravity Q: Adding Mass to Increase G Force & Earth Radius

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To achieve a gravitational acceleration of 10 m/s² on Earth, a significant increase in mass is required, while maintaining the planet's density. Calculations suggest that adding approximately 1.4 times the current mass of Earth would be necessary to reach this gravitational force. This increase would also result in a larger Earth radius, although specific figures depend on the density assumption. Potential sources for this additional mass could include asteroids or other celestial bodies. The discussion highlights the intriguing implications of altering Earth's mass and gravity, inviting creative exploration of the concept.
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Gravity Question??

Jack is tired of having to use 9.8m/s2 all the time to do his calculations concerning gravity. He wants to use a nice round number 10 m/s2. How much mass would have to be added to the Earth to make this happen? What would the new radius of the Earth be? Assume that the density of the Earth will remain the same. Where could you get the mass needed?
 
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Do you have any thoughts on the matter?
 
You know, this would make a good short story...
 
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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