Pulley and Two Masses -- Newton's Law of Motion

[EvilMarisa]

Homework Statement

Pulley's Newton Law of Motion

Relevant Equations

Force = Mass x Acceleration

From this question, I do not understand why there are three forces exerted at Point C (2 of it being the tension by weight A and the other is the tension by weight B) I understand that there is tension by the two weights but why is there 2 forces exerted by weight A at point C?

From the solution, I do not understand the line " if block A moves through Xa to the right then block B moves down through Xb = 1/2 (Xa)". Since this is a pulley, shouldn't the block move at equal distance? My understanding is that Xb should = Xa because it is a pulley and that block B will move based on the distance moved by block A.

 

[haruspex]

From this question, I do not understand why there are three forces exerted at Point C (2 of it being the tension by weight A and the other is the tension by weight B) I understand that there is tension by the two weights but why is there 2 forces exerted by weight A at point C?

The three forces exerted at point C are the weight of the suspended mass and the tension in each of the vertical sections of string. Don't think of the latter as being exerted by the weight on the table. Point C does not 'know' anything about that, it just feels the forces from the string.

From the solution, I do not understand the line " if block A moves through Xa to the right then block B moves down through Xb = 1/2 (Xa)". Since this is a pulley, shouldn't the block move at equal distance? My understanding is that Xb should = Xa because it is a pulley and that block B will move based on the distance moved by block A.

The string has constant length. If A moves to the right by Xa then the string section AD shortens by Xa, but both vertical sections extend by Xb.