A locomotive accelerates a train of identical railway carts. The carts are numbered consecutively with the cart next to locomotive having the number 1. The tension in the connection between the carts

Question

A locomotive accelerates a train of identical railway carts. The carts are numbered consecutively with the cart next to locomotive having the number 1. The tension in the connection between the carts with numbers 4 and 5 is three times bigger than the tension in the connection between the carts with numbers 14 and 15 . What's the number of the last cart? There is no resistance to the train's motion.

TestHub · Accepted Answer

Let the total number of carts be n , each of mass m , acceleration a Tension between carts 4 and 5 pulls the last ( n − 4 ) carts: T 1 ​ = ( n − 4 ) ma Tension between carts 14 and 15 pulls the last ( n − 14 ) carts: T 2 ​ = ( n − 14 ) ma Given T 1 ​ = 3 T 2 ​ : n − 4 = 3 ( n − 14 ) 2 n = 38 ⇒ n = 19

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