A person pulls a rake with 152 Newton of force along the handle. The angle between the handle and the ground is 35.0 degrees. Determine the magnitudes of the horizontal and vertical components of this force.
F = 152N[35o]
Fx = 152*cos35 =
Fy = 152*sin35 =
To determine the magnitudes of the horizontal and vertical components of the force, we can use trigonometric functions.
The horizontal component of the force can be determined using the formula:
Horizontal component = Force * cos(angle)
Substituting the given values:
Horizontal component = 152 N * cos(35.0°)
Using a calculator, the horizontal component of the force is approximately 125.1 Newtons.
The vertical component of the force can be determined using the formula:
Vertical component = Force * sin(angle)
Substituting the given values:
Vertical component = 152 N * sin(35.0°)
Using a calculator, the vertical component of the force is approximately 86.9 Newtons.
Therefore, the magnitudes of the horizontal and vertical components of the force are approximately 125.1 N and 86.9 N, respectively.
To determine the magnitudes of the horizontal and vertical components of the force, we need to use trigonometry.
First, let's identify the given information:
Force applied (F) = 152 Newtons
Angle between the handle and the ground (θ) = 35.0 degrees
Now, let's determine the horizontal and vertical components.
The horizontal component (F_x) represents the force acting parallel to the ground, and the vertical component (F_y) represents the force acting perpendicular to the ground.
To find the horizontal component:
F_x = F * cos(θ)
To find the vertical component:
F_y = F * sin(θ)
Now, let's calculate the values:
F_x = 152 N * cos(35.0°)
F_x ≈ 152 N * 0.819
F_x ≈ 124.888 N
F_y = 152 N * sin(35.0°)
F_y ≈ 152 N * 0.574
F_y ≈ 87.368 N
Therefore, the magnitude of the horizontal component is approximately 124.888 Newtons, and the magnitude of the vertical component is approximately 87.368 Newtons.