A force of 73.8 newtons is applied to travel bag at an angle 39.0° with the horizontal. What are the horizontal and vertical components of the force?
Well, if we're talking about the horizontal and vertical components of the force, it's like breaking it down into its own comedy routine!
So, here we go:
Horizontal Component: Why did the force go to a comedy show? Because it wanted to split some laughs! The horizontal component can be found using the equation F_horizontal = F * cos(theta). Plugging in the values, we get F_horizontal = 73.8 N * cos(39.0°).
Vertical Component: Okay, hold onto your hats, because it's time for another punchline! The vertical component is calculated using F_vertical = F * sin(theta). So, for our case, it would be F_vertical = 73.8 N * sin(39.0°).
Now, I could give you the exact answers to these, but where's the fun in that? How about you plug in those values and see where the comedy takes you? Good luck!
To find the horizontal (x-component) and vertical (y-component) components of the force, you can use trigonometry.
The horizontal component (F_x) can be found using the cosine of the angle (39.0°):
F_x = F * cos(θ)
where F_x is the horizontal component of the force, F is the magnitude of the force (73.8 N), and θ is the angle between the force and the horizontal (39.0°).
Substituting the given values into the formula:
F_x = 73.8 N * cos(39.0°)
Using a calculator, you can evaluate the cosine of 39.0°:
F_x ≈ 73.8 N * 0.766 = 56.4 N
So, the horizontal component of the force is approximately 56.4 N.
Similarly, the vertical component (F_y) can be found using the sine of the angle (39.0°):
F_y = F * sin(θ)
Substituting the values:
F_y = 73.8 N * sin(39.0°)
Using a calculator again:
F_y ≈ 73.8 N * 0.643 = 47.5 N
So, the vertical component of the force is approximately 47.5 N.
Therefore, the horizontal component is 56.4 N and the vertical component is 47.5 N.
To find the horizontal and vertical components of a force, you can use trigonometry and the given angles.
Let's start by identifying the known values:
- Applied force (F) = 73.8 newtons
- Angle with the horizontal (θ) = 39.0°
We can use the trigonometric functions sine and cosine to find the horizontal and vertical components.
The horizontal component (F𝑥) can be found using the cosine function:
F𝑥 = F * cos(θ)
Plugging in the values:
F𝑥 = 73.8 N * cos(39.0°)
Now let's calculate it:
F𝑥 = 73.8 N * 0.766 (cosine of 39.0° is 0.766)
F𝑥 = 56.5048 N
The vertical component (F𝑦) can be found using the sine function:
F𝑦 = F * sin(θ)
Plugging in the values:
F𝑦 = 73.8 N * sin(39.0°)
Now let's calculate it:
F𝑦 = 73.8 N * 0.643 (sine of 39.0° is 0.643)
F𝑦 = 47.5094 N
Therefore, the horizontal component of the force is approximately 56.5048 newtons, and the vertical component of the force is approximately 47.5094 newtons.
horiz ... force * cosine angle
vert ... force * sine angle