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 begger than the tension in the connection between the carts with numbers 14 and 15. What is the number of the last cart? there is no resistance to the train's motion.

Explanation

Acceleration of each cart will be same

Tension in connection between 4 and 5 cart.
`T_(4,5)=m(n-4)a`…(i)
Tension in connection between 14 and 15
`T_(14,15)=m(n-14)a` …(ii)
Given `T_(4,5)=3T_(14.15)`
`M(n-4)a=3m(n-14)aimplies n=19`.