Question

A horizontal cord is attached to a 6.0-𝑘𝑔 body in a horizontal table. The cord passes over a pulley at the end of the table, and to this end is hung a body of mass 8 𝑘𝑔. Find the distance the two bodies will travel after 2𝑠 if they start from rest. What is the tension in the cord?

Answer 1

Write equations that combine forces acting on the M=8- and m=6-kg-body:

$$-Ma=-Mg+T,\\ ma=T.\\\space\\ a=g\frac{M}{M+m}.$$

The distance is

$$d=\frac{at^2}2=\frac{Mgt^2}{2(M+m)}=11.2\text{ m}.$$