Collision between a steel plate and meterstick in frame S?

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A thin steel plate with a circular hole moves parallel to the xz plane in the +y direction, while a meterstick moves in the x direction at a speed of v/c. The plate and meterstick reach the origin of frame S simultaneously, prompting the question of whether a collision occurs. The hole's diameter remains unchanged due to its motion in the y-direction, while the meterstick experiences length contraction in the x-direction. However, when viewed from the meterstick's frame, the steel plate appears to have a relativistic change in its position. Ultimately, the analysis indicates that there will be no collision between the two objects.
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A very thin steel plate with a circular hole one meter in diameter centered on the y-axis lies parallel to the xz plane in frame S and moves in the +y direction at constant speed v, a mterstick lying on the x-axis moves in the x directoin with v/c.The steel plate arrives at the y=0 plane at the same instant teh center of the meterstick reaches the origin of S. Will there be a collision?
 
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Not all that paradoxical. The steel plate (more specifically, the hole) moves in the y-direction so there is no relativistic change in the diameter of the hole. The meter stick is moving in the x direction so there is contraction. By the way, (although it doesn't affect the answer) are you sure about that "with v/c"? Was that "with speed v/c"? In that case, what are the units?
 
yeah, but if you see it in the meter stick' coordinate, then the steel plate does have a relativisic change: it moves in the x direction
 
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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