When Can You Pretend All the Mass is at the Center of Mass?

AI Thread Summary
The discussion centers on when it is appropriate to treat an object's mass as concentrated at its center of mass. It highlights that this simplification is useful for analyzing the motion of extended objects, especially when different parts are moving at varying speeds. However, it notes that in scenarios like car crash testing or analyzing forces on airplanes, treating the object as a single point mass may not be accurate. The conversation reflects on the practical applications of center of mass in real-world situations, particularly in human movement and engineering contexts. Understanding these limitations is crucial for accurate modeling in physics.
Dr_bug
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Homework Statement


Discuss when you can and can’t “pretend all the mass of an object is concentrated at the center of mass”.

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The Attempt at a Solution


So I don't really understand what this is supposed to mean. I know that you utilize center of mass when trying to describe the motion of an extended object where different parts of the object is moving with different speeds. But so far i haven't come across anything you really couldn't use this... and explosion problem maybe... i don't really know and would appreciate some input thanks
 
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Maybe when explaining the motion of large objects, like aeroplanes or human movements
 
well you actually do use center of mass to describe human movements because that's an example that my textbook uses...
 
Dr_bug said:
well you actually do use center of mass to describe human movements because that's an example that my textbook uses...

Well I meant like in testing car crashes, I don't think they consider the entire body as one point mass.


OR analysis of the forces on an aeroplane.
 
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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