add these two forces
a. 200 newtons @ 20 degrees N of E
B. 200 Newtons @ 30 S of E
To add these two forces, we need to express them in terms of their horizontal and vertical components. The horizontal component will be represented by the subscript "x" and the vertical component by the subscript "y". Let's break down each force:
Force A:
Magnitude (A) = 200 N
Angle (θ) = 20 degrees
Direction: North of East
To determine the horizontal and vertical components of Force A, we can use basic trigonometry. Since the angle is given North of East, we need to find the components parallel and perpendicular to the East direction:
Horizontal component (Aₓ): A * cos(θ)
Aₓ = 200 N * cos(20°)
Vertical component (Aᵧ): A * sin(θ)
Aᵧ = 200 N * sin(20°)
Force B:
Magnitude (B) = 200 N
Angle (θ) = 30 degrees
Direction: South of East
Again, we need to find the horizontal and vertical components of Force B, this time parallel and perpendicular to the East direction:
Horizontal component (Bₓ): B * cos(θ)
Bₓ = 200 N * cos(30°)
Vertical component (Bᵧ): B * sin(θ)
Bᵧ = 200 N * sin(30°)
Now that we have calculated the components of each force, we can add them together.
Horizontal component (Resultant Rₓ): Aₓ + Bₓ
Vertical component (Resultant Rᵧ): Aᵧ + Bᵧ
Finally, we can find the magnitude and angle of the resultant force using the components:
Magnitude of the resultant force (R): sqrt(Rₓ² + Rᵧ²)
Angle of the resultant force (θᵣ): tan^(-1)(Rᵧ / Rₓ)
By following these steps, you can calculate the resultant force formed by combining the given forces.