Dan applies a force of 92 N on a heavy box by using a rope held at an angle of 45 degrees with the horizontal. What are the vertical and horizontal components of the 92 N force?
To find the vertical and horizontal components of the force applied by Dan on the box, we can use trigonometric functions.
First, let's define the force magnitude as F = 92 N and the angle with the horizontal as θ = 45 degrees.
To find the vertical component (Fy) of the force, we use the sine function:
Fy = F * sin(θ)
Substituting the given values:
Fy = 92 N * sin(45 degrees)
Using a calculator, sin(45 degrees) is equal to √2/2:
Fy = 92 N * √2/2
Simplifying:
Fy = 46√2 N
Therefore, the vertical component of the force is approximately 46√2 N.
To find the horizontal component (Fx) of the force, we use the cosine function:
Fx = F * cos(θ)
Substituting the given values:
Fx = 92 N * cos(45 degrees)
Using a calculator, cos(45 degrees) is also equal to √2/2:
Fx = 92 N * √2/2
Simplifying:
Fx = 46√2 N
So, the horizontal component of the force is also approximately 46√2 N.