Question

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.

Answer 1

Answer: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 $90^{\circ}$

Net resultant of two forces is

$R=\sqrt{315^2+475^2}$

$R=\sqrt{99225+225625}$

$R=569.95 N \approx 570$

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

$Rcos\theta =475$

$cos\theta =\frac{475}{569.95}=0.833$

$\theta =cos^{-1}(0.833)=33.591$

So replacing two force we can apply a force of magnitude of 570 N at angle of $33.6 ^{\circ}$ with west