A warehouse worker pushes a crate along the floor, as shown in the figure (Figure 1) , by a force of 9.0N that points downward at an angle of 45∘ below the horizontal.
Q1 Find the horizontal component of the push
Q2 Find the vertical component of the push.
both are 9*0.7071
since sin = cos = 0.7071 at 45 degrees.
9cos45 = horizontal
9sin45 = vertical
To find the horizontal and vertical components of the push force, we will use trigonometry.
Given:
Magnitude of the force, F = 9.0 N
Angle below the horizontal, θ = 45°
Let's find the horizontal component of the push force:
Q1. Find the horizontal component of the push:
The horizontal component of a force can be determined using the cosine function:
Horizontal component (F_h) = F * cos(θ)
Substituting the given values:
F_h = 9.0 N * cos(45°)
Using the cosine of 45° (which is equal to √2 / 2):
F_h = 9.0 N * (√2 / 2)
Simplifying:
F_h = (9.0 N * √2) / 2
Therefore, the horizontal component of the push force is (4.5 N * √2).
Now, let's find the vertical component of the push force:
Q2. Find the vertical component of the push:
The vertical component of a force can be determined using the sine function:
Vertical component (F_v) = F * sin(θ)
Substituting the given values:
F_v = 9.0 N * sin(45°)
Using the sine of 45° (which is equal to √2 / 2):
F_v = 9.0 N * (√2 / 2)
Simplifying:
F_v = (9.0 N * √2) / 2
Therefore, the vertical component of the push force is (4.5 N * √2).
To find the horizontal and vertical components of the push force, we can use trigonometric ratios. Let's break down the given information:
Force magnitude = 9.0 N
Angle below the horizontal = 45°
Q1: To find the horizontal component of the push (Fx):
We know that the horizontal component (Fx) is equal to the force magnitude (F) multiplied by the cosine of the angle (θ).
1. Identify the given values:
- Force magnitude (F) = 9.0 N
- Angle (θ) = 45°
2. Apply the formula:
Fx = F * cos(θ)
3. Substitute the values and calculate:
Fx = 9.0 N * cos(45°)
Fx ≈ 9.0 N * 0.7071
Fx ≈ 6.36 N
Therefore, the horizontal component of the push force is approximately 6.36 N.
Q2: To find the vertical component of the push (Fy):
We know that the vertical component (Fy) is equal to the force magnitude (F) multiplied by the sine of the angle (θ).
1. Identify the given values:
- Force magnitude (F) = 9.0 N
- Angle (θ) = 45°
2. Apply the formula:
Fy = F * sin(θ)
3. Substitute the values and calculate:
Fy = 9.0 N * sin(45°)
Fy ≈ 9.0 N * 0.7071
Fy ≈ 6.36 N
Therefore, the vertical component of the push force is approximately 6.36 N.