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Mariana
1 day ago
12

The resultant of the concurrent forces is 300 lb pointing up along the Y axis. Compute the values of F and the angle required to

give the resultant.

Physics
2 answers:
Yuliya22 [1.1K]1 day ago
5 0

The computed values of F and the angle that would yield the resultant are F = 823.529 lbs and theta = 30.667 degrees.

Further Clarification

The resultant force from the concurrent efforts is 300 lb directed upwards along the Y axis. We need to find F and the corresponding angle.

The initial step is to determine the x and y components of all forces and then focus on the isolated figure:

The total of y components is

\sum F_y = R_y\\F sin \theta - (240 lbs) (sin 30) = 300 lbs\\F sin \theta - (240 lbs) (0.5) = 300 lbs\\F sin \theta - (120 lbs) = 300 lbs\\F sin \theta = 420 lbs

The total of x components is

\sum F_x = R_x\\F cos \theta - (240 lbs) (cos 30) - 500 lbs = 0\\F cos \theta - (240 lbs) (0.866) - 500 lbs = 0\\F cos \theta - (207.846 lbs) - 500 lbs = 0\\F cos \theta = 707.846 lbs

By substituting the angle θ in either of the two working equations, we can obtain

\frac{F sin \theta}{F cos \theta} = \frac{420 lbs}{707.846 lbs} \\tan \theta = 0.593\\\theta = 30.667 \\ F sin \theta = 420 lbs\\F sin 30.667 = 420 lbs\\F = \frac{420 lbs}{sin 30.667} \\F = \frac{420 lbs}{0.510} \\F = 823.529 lbs

Learn More

  1. Find out more about the values of F
  2. Discover more about the resultant
  3. Learn more about the angle

Answer Details

Grade: 9

Subject: Physics

Chapter: Forces

Keywords: values of F, angle, resultant, concurrent forces, angle

Maru [1K]1 day ago
5 0
<span>500 cos(180) i + 500 sin(180)
240 cos(-30) i + 240 sin(-30)
F cos(theta) i + F sin(theta)
-----------------------------------
300 cos(90) i + 300 sin(90)</span>
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