Two ropes are attached to a heavy box to pull it along the floor. one rope applies a force of 475 newtons in a direction due west; the other applies a force of 315 newtons in a direction due south. as we will see later in text, force is a vector quantity. how much force should be applied by a single rope and in what direction (relative to due west) if it is to accomplish the same effect as the two forces added together.

570 N

Explanation:

Given

one rope applies a force of 475 N in west direction

other applies a force of 315 N in south direction

So both forces are at an angle of

Net resultant of two forces is

and the resultant will be an angle of \theta with 475 Newton force

So replacing two force we can apply a force of magnitude of 570 N at angle of with west

the box does not move because you need to use a force greater than 300 n. you are only using 50 n. it needs to at least be 301 n for the box to move because then it is an unbalanced force and it will move the way that the greater force is pushing it. if you use only 300 n it will be a balanced force and will not move because the force you are exerting on the   box is the same as its force.

hope this !

im sorry if i went too in depth, i am going to include a link to a video on khan academy that will explain this.   hope that you like the video and that it explains more in detail to you.

that is the link.