Free body diagrams of forces, forces expressed by their components and Newton's laws are used to solve these problems.
Problems involving forces of friction and tension of strings and ropes are also included.
The following are a bunch of pulley exercises and problems.
If you can work through and understand them you should be able to solve most standard pulley problems.
This tension will be pulling the three kilogram, trying to make it move, but it opposes the motion of the five kilogram mass, and if we think of this three plus five kilogram mass as a single object, these end up just canceling on our single object that we're viewing as one big eight kilogram mass. We don't include them, they're not part of this trick.
We have to figure out what other forces would try to make this system go or try to prevent it from moving.
And that's trying to prevent the system from moving. And the total mass is just five plus three, is gonna be eight kilograms, and I get the acceleration of my system.
This five kilogram mass is accelerating downward, and this force is in the opposite direction of motion. They're like, I don't understand, they're both pointing down. They would when we're using Newton's second law the way we usually use it, but when we're using this trick, what we're concerned with are forces in the direction of motion, this is an easy way to figure it out, forces in the direction of motion we're gonna call positive. Because all the motion in the system is this way, we'd find that way's positive, but this force of gravity on the three kilogram mass is the opposite direction. It's preventing the system from accelerating as fast as it would have. So if I just add this up, I get 2.45 meters per second squared.
This is a quick way to get what the magnitude of the acceleration is of the objects in my system, but it's good to note, it'll only work if the objects in your system are required to move with the same magnitude of acceleration.
And in this case they are, what I have here is a five kilogram mass tied to a rope, and that rope passes over a pulley, pulls over and connects to this three kilogram mass so that if this five kilogram mass has some acceleration downward, this three kilogram mass has to be accelerating upward at the same rate, otherwise this rope would break or snap or stretch, and we're assuming that that doesn't happen.