Answer to Question #155871 in Physics for muhammad tajammal

Question #155871

A rope is tied to the top of a 10 m flag pole. The rope is tensioned to 120N and then tied to a stake in the ground 20m from the bottom of the pole. The ground is level. Find the vertical and horizontal components of this force.


1
Expert's answer
2021-01-16T17:23:49-0500


The situation is shown in the figure. From the right triangle ABC\triangle ABC, obtain:

AB=CB2+AC2=102+202=105mAB = \sqrt{CB^2 + AC^2} = \sqrt{10^2 + 20^2} = 10\sqrt{5}m

The vertical projection of the force F\mathbf{F} is:


Fv=FsinθF_v = F\sin\theta

According to the sine definition, obtain:


Fv=FCBAB=12010105=1205=245NF_v = F\dfrac{CB}{AB} = 120\dfrac{10}{10\sqrt{5}} = \dfrac{120}{\sqrt{5}} = 24\sqrt{5}N

The horizontal projection is (according to the cosine definition):


Fh=Fcosθ=FACAB=12020105=485NF_h = F\cos\theta= F\dfrac{AC}{AB} = 120\dfrac{20}{10\sqrt{5}} = 48\sqrt{5}N

Answer. Horizontal 485N48\sqrt{5}N, vertical 245N24\sqrt{5}N.


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