Question

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.

Answer 1

500 cos(180) i + 500 sin(180)
240 cos(-30) i + 240 sin(-30)
F cos(theta) i + F sin(theta)
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300 cos(90) i + 300 sin(90)

Answer 2

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

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

The sum of x components is

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

Substitute the value of θ to either of the two working equations, we have

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

Learn more

1. Learn more about the values of F brainly.com/question/12251772
2. Learn more about The resultant brainly.com/question/11784431
3. Learn more about  the angle 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