Can the kinetic energy of a system be negative?

AI Thread Summary
Kinetic energy (KE) cannot be negative since mass is always positive and velocity squared eliminates any negative values. In contrast, gravitational potential energy can be negative based on the chosen reference point for zero potential. However, the critical aspect is that only changes in potential energy affect kinetic energy and the forces involved. Therefore, while KE is always non-negative, gravitational potential energy can vary depending on the system's reference frame. Understanding these principles is essential for analyzing energy transformations in physical systems.
meredith
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what about the gravitational potential energy of a system?

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Nope. Think of the formula for KE. Mass is never negative, and even if the velocity is negative, its squared so the negative sign goes away.

Gravitational Potential can be negative depending on where you define your potential to be zero. But really, only changes in potential energy are relevant. Its only when the gravitational potential energy changes that the KE changes, a force is exerted, etc.
 
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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