Newton's Laws Audio Guided Solution NL20Q7

This problem could be classified as a two-body problem in which there's two masses accelerating together in the same direction, the direction in this case being down. There are also two ropes in this in this problem and so I'm going to refer to the ropes as top rope and bottom rope and what we wish to find in the problem is the tension in the bottom rope. Now as we approach problems like these typically what we do is we perform a system analysis to relate the forces upon the system to the acceleration of the system and then we perform an individual body analysis in which we relate the forces upon either one of our objects to the acceleration of the object. Now in this particular problem we already know the acceleration of the object and it's 5.05 meters per second squared which would mean we would probably be able to skip the part of the problem where we do the system analysis and what we wish to do is find the tension in the rope between the masses and so since that rope is the only rope attached to the bottom mass I'm just going to focus on the bottom mass at 3.4 kilogram mass and do an individual body analysis on the 3.4 kilogram mass. So if I draw the forces upon it there's just two, there's gravity down and then there's tension up and it's the tension that I wish to find in this problem. So I think this is going to be quite easy for us. We can say for the lower mass or bottom mass since it's accelerating downwards I'll take the force downwards minus the force upwards that's the force in the direction of acceleration minus the one that opposes it so I'll go 3.4 times 9.8 minus F tension equal 3.4 times 5.05 equal ma and you solve for F tension and it isn't that easy. Good luck to you.