Solve Relativity Problem - Find Speed of Ref. Frame

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To solve the relativity problem of finding the speed of a reference frame where two events occur simultaneously, one must apply the Lorentz transformation equations. Given two events 100 meters apart with a time interval of 0.30 microseconds, the goal is to find a speed v that makes the time coordinate of the second event zero in the moving frame. This involves setting the transformed time equation t'_B to zero and solving for v using the provided Lorentz transformation formulas. The discussion emphasizes the need to relate time and distance through these transformations to achieve simultaneity in the new reference frame. Understanding and applying these principles is crucial for solving the problem effectively.
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In a particular reference frame, two events occur 100m apart, with an intervening time interval of 0.30us . The speed of a reference frame in which they occur simultaneously is ?

anyone can tell me how to slove this problem? I don't have any idea about it . Thanx
 
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you need to find a frame of reference where the time interval between events becomes zero.
 
Rioluany said:
In a particular reference frame, two events occur 100m apart, with an intervening time interval of 0.30us.
Let the occurence of event A have coordinates (x,y,z,t) = (0,0,0,0) in this frame, f. Event B will have coordinates (x_B,y_B,z_B,t_B) = (100,0,0,.30) (times in us.)

The speed of a reference frame in which they occur simultaneously is ?
Consider another frame of reference, f', moving parallel to the direction of the displacement between Event A and Event B with speed v and with its origin at Event A (i.e in this frame the coordinates of Event A are (x',y',z',t') = (0,0,0,0))

We want to set v so that the coordinates of Event B in f' are (x'_B,y'_B,z'_B,t'_B) = (x'_B,0,0,0)


Times and distances in these frames are related by the Lorentz transformation:

(1)t'_B = \gamma (t_B - vx_B/c^2)
(2)x'_B = \gamma (x_B - vt)

So determine v if:
t_B' = 0

AM
 
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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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