Understanding the Work of Gravity: Exploring Positive and Negative Forces

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When two massive objects are moved directly away from each other, the work done by the force of gravity is negative for both objects, not positive for one and negative for the other. The reasoning behind this is that gravitational force acts to pull the objects together, so moving them apart requires work against this force. If the objects were moved closer together, the work done would indeed be positive, as gravity assists in their movement. Therefore, the statement is false because the work done is consistently negative when moving apart. Understanding these dynamics is crucial for grasping the principles of gravitational forces.
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Homework Statement


( True / False ) When two massive objects are moved directly away from each other the work done by the force of gravity between the objects is positive for one of the objects and negative for the other.

The Attempt at a Solution



i believe the answer to be false because both will always be negative
 
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Your reasoning is OK, but always? What if the objects are moved closer together?
 
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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