The 27-kg slider block is moving to the left with a speed of 5 m/s when it is acted upon by the forces $F_1$ and $F_2$. Neglect friction and the mass of the pulleys and cords.
The net force acting on the object by the ropes should be $4F_1 - 1F_2$ according to the solution manual. I guess I never fully understood how different tensions act on objects. I understand intutitvely that there should be only $1F_2$ force acting on the box on the left because the string pulls on the box with exactly $1F_2$ force.
But for the right portion of the box diagram where $F_1$ is acting on the object. Why is it $4F_1$ exactly? I am just trying to intuitively make sense out of the equation as opposed to just counting ropes. This may be a real simple question but please help me out.
Edit: I am not asking for a hw solution (I have access to the solution manual), I am simply asking for a deeper explanation on how tensions act as forces in this diagram to solidify my understanding.