Two Forces A And B Act On An Object. Force A Is 85 N And Is At An Angle Of 20 Degrees To The Horizontal.Force B Is 125 N And Is At An Angle Of 60 Degrees To The Horizontal. Find component Force Of Vector A?
Horizontal component of A = 85 cos 20 Newtons
Vertical component of A = 85 sin 20 Newtons
To find the component force of vector A, we need to decompose the force into its horizontal and vertical components.
Given:
Magnitude of Force A, |A| = 85 N
Angle with the horizontal, θ = 20 degrees.
To find the horizontal component of vector A, we can use the cosine function:
Horizontal Component of A, Ax = |A| * cos(θ)
Substituting the given values:
Ax = 85 N * cos(20 degrees)
Using a calculator:
Ax ≈ 85 N * 0.9397 ≈ 79.9525 N
Therefore, the component force of vector A in the horizontal direction is approximately 79.9525 N.
To find the component force of Vector A, we need to break it down into its horizontal (x-axis) and vertical (y-axis) components.
Given:
Force A = 85 N
Angle of Force A with the horizontal = 20 degrees
To find the horizontal component of Force A:
Horizontal component of Force A = Force A * cos(angle)
Horizontal component of Force A = 85 N * cos(20 degrees)
Using a calculator, we find that the cos(20 degrees) ≈ 0.9397
Horizontal component of Force A = 85 N * 0.9397
Horizontal component of Force A = 79.9565 N (approximately 80 N)
Therefore, the horizontal component of Force A is approximately 80 N.
Note: The horizontal component represents the force acting parallel to the x-axis.
To find the vertical component of Force A:
Vertical component of Force A = Force A * sin(angle)
Vertical component of Force A = 85 N * sin(20 degrees)
Using a calculator, we find that the sin(20 degrees) ≈ 0.3420
Vertical component of Force A = 85 N * 0.3420
Vertical component of Force A = 29.0700 N (approximately 29 N)
Therefore, the vertical component of Force A is approximately 29 N.
Note: The vertical component represents the force acting parallel to the y-axis.
So, the component force of Vector A is approximately 80 N horizontally and 29 N vertically.