The values of F and the angle required to give the resultant are F = 823.529 lbs and theta = 30.667 degrees
Further explanation
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.
The first thing is to get the x and y components of each forces, then isolate the given figure:
The sum of y components is
[tex]\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[/tex]
The sum of x components is
[tex]\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[/tex]
Substitute the value of θ to either of the two working equations, we have
[tex]\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 [/tex]
Learn more
- Learn more about the values of F https://brainly.com/question/12251772
- Learn more about The resultant https://brainly.com/question/11784431
- Learn more about the angle https://brainly.com/question/10217662
Answer details
Grade: 9
Subject: physics
Chapter: forces
Keywords: the values of F, the angle, The resultant, the concurrent forces, angle
