A child pulls a wagon along level ground. The handle with which she pulls the wagon makes an angle of 20.0 degrees with the ground as the child pulls with a force of 78.0 Newton. What are the components of the force. Pls pls pls pls help me answer this and may God bless u!
Same procedure as previous post
To find the components of the force, we need to break the force down into its horizontal and vertical components.
Given:
Angle with the ground (θ) = 20.0 degrees
Force (F) = 78.0 Newton
To find the horizontal component:
Horizontal component (F_x) = F * cos(θ)
To find the vertical component:
Vertical component (F_y) = F * sin(θ)
Let's plug in the values and calculate the components:
Horizontal component (F_x) = 78.0 N * cos(20.0°)
Vertical component (F_y) = 78.0 N * sin(20.0°)
Calculating:
F_x = 78.0 N * cos(20.0°)
F_x ≈ 73.828 N
F_y = 78.0 N * sin(20.0°)
F_y ≈ 26.62 N
Therefore, the components of the force are approximately:
Horizontal component (F_x) ≈ 73.828 Newton
Vertical component (F_y) ≈ 26.62 Newton
To determine the components of the force, we can break the force vector into horizontal and vertical components. The horizontal component will be the force that acts parallel to the ground, and the vertical component will be the force that acts perpendicular to the ground.
First, let's find the horizontal component. To do this, we need to find the cosine of the angle. The cosine of an angle is equal to the adjacent side divided by the hypotenuse. In this case, the adjacent side is the horizontal component of the force, and the hypotenuse is the magnitude of the force (78.0 Newton).
So, the horizontal component (F_horizontal) can be calculated as:
F_horizontal = F * cos(angle)
Substituting the given values:
F_horizontal = 78.0 N * cos(20.0 degrees)
Now, let's find the vertical component. To do this, we need to find the sine of the angle. The sine of an angle is equal to the opposite side divided by the hypotenuse. In this case, the opposite side is the vertical component of the force, and the hypotenuse is the magnitude of the force (78.0 Newton).
So, the vertical component (F_vertical) can be calculated as:
F_vertical = F * sin(angle)
Substituting the given values:
F_vertical = 78.0 N * sin(20.0 degrees)
Now you can calculate the values of both components by evaluating the trigonometric functions:
F_horizontal = 78.0 N * cos(20.0 degrees)
F_vertical = 78.0 N * sin(20.0 degrees)
So, the horizontal component of the force is equal to F_horizontal and the vertical component is equal to F_vertical, where F is the force magnitude (78.0 N) and the angle is 20.0 degrees.