A Body Is In Equilibrium When Three Forces Act On It,two Of The Forces Are F1 Of Magnitude 8n Acting Dud East And F2 Which Is 5n Acting N60degree East.Find The Magnitude And Direction Of The Third Force.
You want <x,y> such that
<8,0>+<5cos30°,5sin30°>+<x,y> = <0,0>
then you can get the direction of <x,y>
To find the magnitude and direction of the third force, we can use the concept of vector addition and solve for the resultant force.
Step 1: Draw a diagram.
Draw a coordinate system and mark the two given forces F1 and F2. Since F1 is directed due east, draw it along the positive x-axis. F2 is directed at an angle of 60 degrees north of east.
Step 2: Decompose F2 into its x and y components.
F2 can be decomposed into its x and y components using trigonometry. The x-component (F2x) can be found by multiplying the magnitude of F2 (5 N) by the cosine of the angle (60 degrees). The y-component (F2y) can be found by multiplying the magnitude of F2 (5 N) by the sine of the angle (60 degrees).
F2x = 5 N * cos(60 degrees)
F2y = 5 N * sin(60 degrees)
Step 3: Calculate the x-component of the third force.
Since the body is in equilibrium, the net force in the x-direction must be zero. Therefore, the x-component of the third force (F3x) should cancel out the x-components of F1 and F2.
F3x = - F1x - F2x
Step 4: Calculate the y-component of the third force.
Since the body is in equilibrium, the net force in the y-direction must be zero. Therefore, the y-component of the third force (F3y) should cancel out the y-components of F1 and F2.
F3y = - F1y - F2y
Step 5: Calculate the magnitude and direction of the third force.
The magnitude of the third force (F3) can be found using the Pythagorean theorem:
F3 = sqrt(F3x^2 + F3y^2)
The direction of the third force (angle theta) can be found using trigonometry:
theta = atan(F3y/F3x)
By plugging in the values for F1x, F1y, F2x, and F2y into the above equations, we can calculate the magnitude and direction of the third force.