Why do 2 crates pulled together have the same acceleration?

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When a force F is applied to crate 1, both crates accelerate together due to the tension in the rope connecting them. Since crate 1 and crate 2 are linked, they must have the same acceleration to maintain the rope's tautness, which is 2.5 m/s² in this scenario. If crate 2 were to accelerate differently, the rope would either slack or become taut, contradicting the fixed length condition. The situation can be analyzed using force diagrams, showing that the net force acting on both crates results in the same acceleration. Therefore, both crates experience the same acceleration due to their connection and the absence of friction.
Josh114
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Hi. I was given the classic problem of a woman pulling crate 1 on a frictionless surface with a force F, which is attached to crate2 behind it with a rope. crate 1=6kg, crate 2= 4kg, and it says crate 1 has an acceleration of 2.5m/s^2...
One question asks for the acceleration of crate 2, and the answer is 2.5m/s^2, but I'm confused as to why they have the same acceleration. Could it be proved with force diagrams or with math?
Thanks

Attempt:
None. It's a conceptual problem, so there's no work to show
 
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If the rope is of fixed length and pulled tight what is velocity of crate 2 compared to crate 1 ? Less than , greater than or equal to ?
 
What happens if the acceleration is not the same for both crates?
 

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