(A) The following forces are acting at a point. 1)450N force towards north-east. 2)350N force towards east. 3)250N force at 30º west of north. 4)300N force at 60º south of west. Find magnitude and direction of the resultant
i need all steps detailed
I get 480 @ N55ºE
To find the magnitude and direction of the resultant force, we need to add all the given forces vectorially.
Step 1: Represent the given forces as vectors
Let's represent the four forces mentioned in the question as vectors:
1) 450N force towards north-east: This force can be split into two perpendicular components. One component is directed towards the north, and the other is directed towards the east. We can find these components using trigonometry. Let's call these components F₁ and F₂.
Using a right-angled triangle formed by these components, we can find:
F₁ = 450N * cos(45º)
F₂ = 450N * sin(45º)
2) 350N force towards the east: Since this force is directed entirely towards the east, we can represent it as (350N, 0º).
3) 250N force at 30º west of north: We can represent this force as (250N, -30º) since it is 30º in the clockwise direction from the north.
4) 300N force at 60º south of west: We can represent this force as (300N, 210º) since it is 60º in the clockwise direction from the west.
Step 2: Add the vectors
Add all the force vectors together by adding their horizontal and vertical components separately:
Horizontal component: Sum up all the horizontal components of the vectors.
Vertical component: Sum up all the vertical components of the vectors.
Step 3: Find the magnitude and direction of the resultant force
Using the horizontal and vertical components found in the previous step, we can calculate the magnitude of the resultant force (R) using the Pythagorean theorem:
R = √(horizontal component^2 + vertical component^2)
To find the direction (θ) of the resultant force, we can use trigonometry:
θ = tan^(-1)(vertical component / horizontal component)
By following these steps, you should be able to calculate both the magnitude and direction of the resultant force based on the given forces.