Find the resultant of 50 N acting east and 30 N acting 30 degrees northeast
Fr = 50N.[0o] + 30[30o].
X = 50 + 30*Cos30 = 76.0 N.
Y = 30*sin50 = 15 N.
Tan A = Y/X = 15/76 = 0.19737.
A = 11.2o
Fr = X/Cos A = 76/Cos11.2 = 77.5 N.]11.2o] N. of E.
To find the resultant of two forces, we can use vector addition. We will break down each force into its horizontal and vertical components, and then add those components to determine the resultant.
Let's start by finding the horizontal and vertical components of each force.
Force acting east (50 N):
Since this force is acting directly in the east direction, its horizontal component (Fx) will be 50 N and its vertical component (Fy) will be 0 N.
Force acting 30 degrees northeast (30 N):
To find the horizontal and vertical components of this force, we need to resolve it into its x and y components based on the given angle.
The horizontal component (Fx) can be found using the cosine of the angle:
Fx = 30 N * cos(30°) ≈ 26 N
The vertical component (Fy) can be found using the sine of the angle:
Fy = 30 N * sin(30°) ≈ 15 N
Now that we have the horizontal and vertical components of both forces, let's add them together to find the resultant.
Horizontal component sum (Rx):
Rx = Fx1 + Fx2
= 50 N + 26 N
= 76 N
Vertical component sum (Ry):
Ry = Fy1 + Fy2
= 0 N + 15 N
= 15 N
The resultant force (R) can be found using the Pythagorean theorem:
R = √(Rx^2 + Ry^2)
= √(76 N^2 + 15 N^2)
≈ √(5776 + 225)
≈ √6001
≈ 77.46 N
Therefore, the resultant of the two forces is approximately 77.46 N.