A particle is acted upon a body by the following forces:
55N Towards East,45N inclined at(E 80 Degrees Towards North East),50N Towards North East, 60N inclined at (E 20 Degrees towards South of West),40N Towards South.
Determine the magnitude and direction of the resultant force.
break these up into two components
N direction: and E direction:
I can't follow your designations on direction.
To determine the magnitude and direction of the resultant force, we first need to resolve each force into its horizontal and vertical components.
Let's break down the given forces:
1. 55N Towards East: This force only has a horizontal component and its value is 55N.
2. 45N inclined at (E 80 Degrees Towards North East): To find the horizontal and vertical components of this force, we'll use the sine and cosine functions.
The horizontal component = 45N * cos(80°)
The vertical component = 45N * sin(80°)
3. 50N Towards North East: This force has both horizontal and vertical components. To find them, we'll again use the sine and cosine functions.
The horizontal component = 50N * cos(45°)
The vertical component = 50N * sin(45°)
4. 60N inclined at (E 20 Degrees towards South of West): Similar to the second and third forces, we'll use sine and cosine to find the horizontal and vertical components.
The horizontal component = 60N * cos(20°)
The vertical component = 60N * sin(20°)
5. 40N Towards South: This force only has a vertical component and its value is -40N (negative because it acts in the opposite direction of the positive y-axis).
Now, let's calculate the horizontal and vertical components for each force:
1. Horizontal component = 55N * cos(0°) = 55N
Vertical component = 55N * sin(0°) = 0N
2. Horizontal component = 45N * cos(80°) ≈ 9.292N
Vertical component = 45N * sin(80°) ≈ 42.761N
3. Horizontal component = 50N * cos(45°) ≈ 35.355N
Vertical component = 50N * sin(45°) ≈ 35.355N
4. Horizontal component = 60N * cos(20°) ≈ 56.232N
Vertical component = 60N * sin(20°) ≈ 20.557N
5. Horizontal component = 0N
Vertical component = -40N
Now, let's find the resultant horizontal and vertical components by adding all the respective components:
Horizontal component = 55N + 9.292N + 35.355N + 56.232N + 0N = 155.879N
Vertical component = 0N + 42.761N + 35.355N + 20.557N + (-40N) = 58.673N
To find the magnitude of the resultant force, we can use the Pythagorean theorem:
Resultant magnitude = √(Horizontal component^2 + Vertical component^2)
Resultant magnitude = √(155.879N^2 + 58.673N^2) ≈ 169.88N
To find the direction of the resultant force, we can use the inverse tangent (arctan) function:
Resultant direction = arctan(Vertical component / Horizontal component)
Resultant direction = arctan(58.673N / 155.879N) ≈ 20.5°
Therefore, the magnitude of the resultant force is approximately 169.88N, and its direction is approximately 20.5°.