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

Answer 2

The magnitude of the resultant force acting on ropes is 570 N and it acts at angle of 33.6 degrees relative to due west direction.

What is force?

Force is the effect of pull or push due to which the object having a mass changes its velocity.

The force is of two types-

• Push-When the force applied in the direction of motion of the object, then the force is called the push force.

• Pull- When the force applied in the opposite direction of motion of the object, then the force is called the pull force.

As one rope applies a force of 475 newtons in a direction due west and the other applies a force of 315 newtons in a direction due south.

Thus, the net force of the two ropes can be given as,

$F=\sqrt{475^2+315^2}\\F\cong570\rm N$

Now this resultant will be at the south-west direction. Let the resultant force acting on the south-west direction at an angle of $\theta$.

Thus, the net resultant force acting relative to due west direction will be,

$F\cos\theta={475}{}\\\cos\theta=\dfrac{475}{570}\\\theta=\cos{-1}(0.833)\\\theta=33.6$

Thus, the magnitude of the resultant force acting on ropes is 570 N and it acts at angle of 33.6 degrees relative to due west direction.

Learn more about the force here;

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