Showing px-Et is invariant using Lorentz Transformations

AI Thread Summary
The discussion focuses on demonstrating the invariance of the quantity px - Et using Lorentz Transformations, where p represents momentum and E represents energy. Participants are encouraged to identify relevant 4-vectors to aid in solving the problem. Initial confusion is expressed regarding how to start the problem effectively. The hints provided suggest considering the relationship between momentum, energy, and time as 4-vectors. The conversation highlights the challenge of applying Lorentz Transformations to prove the invariance of this quantity.
Nitric
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1. Using the Lorentz Transformations, show that the quantity px - Et is invariant, where p and E are the momentum and energy, respectively, of an object at position x at time t.
2. px - Et
3. I needed help on starting the problem. Where should I begin?
 
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Nitric said:
Using the Lorentz Transformations, show that the quantity px - Et is invariant, where p and E are the momentum and energy, respectively, of an object at position x at time t.

Hi Nitric! :smile:

Hint: what 4-vectors can you see in this problem? :wink:
 


tiny-tim said:
Hi Nitric! :smile:

Hint: what 4-vectors can you see in this problem? :wink:
p x E and t?
 
Nitric said:
p x E and t?

erm … nooo :redface:
 


Damn. Well I honestly have no idea, kinda stuck on this problem
 
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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