To find the [tex]\( y \)[/tex]-component of the force acting on the block, we can use the concept of trigonometric decomposition of vectors. Here’s a step-by-step breakdown of the procedure:
1. Identify the given values:
- The magnitude of the force, [tex]\( F \)[/tex], is [tex]\( 124 \)[/tex] Newtons.
- The angle [tex]\( \theta \)[/tex] that the force makes with the horizontal is [tex]\( 29.6^\circ \)[/tex].
2. Recall the formula to find the [tex]\( y \)[/tex]-component of a force:
[tex]\[
F_y = F \sin(\theta)
\][/tex]
Where [tex]\( F_y \)[/tex] is the [tex]\( y \)[/tex]-component of the force, [tex]\( F \)[/tex] is the magnitude of the force, and [tex]\( \theta \)[/tex] is the angle the force makes with the horizontal.
3. Convert the angle from degrees to radians: Since the sine function in most trigonometric calculations is typically defined in radians, we convert [tex]\( 29.6^\circ \)[/tex] to radians.
- However, for simplicity, we assume the angle conversion and sine calculation are handled accurately.
4. Calculate the [tex]\( y \)[/tex]-component:
Using the sine function with the given angle, we have:
[tex]\[
F_y = 124 \sin(29.6^\circ)
\][/tex]
5. Result:
By applying the sine function to the angle [tex]\( 29.6^\circ \)[/tex] and multiplying it by the force magnitude [tex]\( 124 \)[/tex] Newtons, we get:
[tex]\[
F_y \approx 61.24879145644464 \text{ N}
\][/tex]
Thus, the [tex]\( y \)[/tex]-component of the force acting on the block is:
[tex]\[
\overrightarrow{F_y} \approx 61.24879145644464 \text{ N}
\][/tex]
