when resolving gravity into components
Fg (x component) = Fg sin theta
when you get the units you get
Newton times a degree
how come we just ignore the degree
for example if it was 9 N you wouldnt say 9 N (degrees) why not? How do the degrees just magically dissapear not to mention you could use radians and such instead
theta has units of degrees. sin(theta) does not.
When resolving gravity into components, we use trigonometry to break down the force of gravity into its horizontal and vertical components. In this case, the formula you mentioned does not involve degrees as the units for the force itself. Instead, the degrees are used in the trigonometric function to calculate the ratio of the side lengths of a right triangle.
Let me explain the process step by step:
1. First, we have the force of gravity (Fg) acting at an angle (θ) with respect to the horizontal axis. We want to find the horizontal component of this force.
2. To resolve the force of gravity, we use the trigonometric function sine (sin). According to the definition of sine, sin(θ) = opposite/hypotenuse. In this case, the opposite side represents the vertical component of the force (Fg sin θ), and the hypotenuse represents the magnitude of the force.
3. The result of the calculation Fg sin θ gives us the magnitude of the horizontal component of the force. The units for this magnitude will still be in Newtons (N). The degrees themselves are a unit of measurement for angles and are not applicable to the units of force.
4. So, we do not include "degrees" as part of the units for the magnitude of the horizontal component of the force because degrees represent the measure of an angle, not the magnitude of a force.
In summary, the degrees in the formula Fg sin θ are used to determine the ratio between the sides of a right triangle, but they do not appear as units in the final result because they are units of measurement for angles, not forces. You are correct that radian measurements can also be used in mathematical calculations, but in this particular context, degrees are commonly used.