I was given a systems equation. Two masses are on a flat frictionless surface tied together. There is a pulley type thing and another mass is hanging over the edge of the table. It is attatched to the other 2 masses. It has no Fn, only Fg because it is hanging.

So I draw lines of Fg and Fn on the other masses, but they cancel out.

M1=12g
M2=8g
I must find out what T1 and T2 are?
Which are the tensions of the rope/string between each of the masses. The problem says everything is frictionless. But then it says the objects are released from rest. (what does that mean?)

To find the tensions T1 and T2 in the rope/string connecting the masses, you can analyze the forces acting on each mass and use Newton's second law of motion.

First, let's consider the forces acting on the hanging mass M1 (the one with Fg only). In this case, since the surface is assumed to be frictionless, there will be only one force acting on M1, which is its weight or gravitational force (Fg). This force is given by the equation Fg = M1 * g, where g is the acceleration due to gravity.

Next, let's consider the forces acting on the other two masses, M2 and M3, connected by the rope/string. Here, we have two unknown tensions (T1 and T2) acting in opposite directions along the rope/string. Additionally, there will also be gravitational forces acting on each mass.

Now, let's determine the forces acting on M2. It will experience the tension T1 (directed towards M1) and the gravitational force Fg2 = M2 * g. Since the surface is frictionless, there will be no normal force (Fn).

On the other hand, M3 will experience the tension T2 (directed towards M2) and its own weight Fg3 = M3 * g. Similar to M2, M3 will not experience any normal force.

To solve for the tensions T1 and T2, we'll use Newton's second law of motion, which states that the net force acting on an object is equal to its mass multiplied by its acceleration (F = m * a). In this case, we'll take the acceleration of the system to be the same for all masses because they are connected.

Since the system is initially at rest, the acceleration will be zero. Therefore, the net force on each mass will also be zero. We'll set up two equations based on this:

For M1:
Fg = T1

For M2:
T2 - T1 = Fg2

For solving these equations, you can substitute the given values of M1, M2, and g into the equations, and solve for T1 and T2. Once you find their values, you will have determined the tensions in the rope/string connecting the masses.