To find the x-component of the force acting on a block when a force is applied at an angle from the horizontal, we use the cosine component of the force vector along the x-axis. The following steps outline the solution:
1. Understand the given values:
- The magnitude of the force, [tex]\( F \)[/tex], is 177 N.
- The angle, [tex]\( \theta \)[/tex], at which the force is applied from the horizontal is [tex]\( 85.0^{\circ} \)[/tex].
2. Convert the angle from degrees to radians:
Angles are often more conveniently expressed in radians for calculations involving trigonometric functions. The conversion from degrees to radians is done by multiplying the degree measure by [tex]\( \frac{\pi}{180} \)[/tex].
[tex]\[
\theta_{\text{radians}} = 85.0^{\circ} \times \frac{\pi}{180}
\][/tex]
This gives:
[tex]\[
\theta_{\text{radians}} = 1.4835298641951802 \text{ radians}
\][/tex]
3. Calculate the x-component of the force:
The x-component of the force can be found using the formula [tex]\( F_X = F \cos(\theta) \)[/tex], where [tex]\( F \)[/tex] is the magnitude of the force and [tex]\( \theta \)[/tex] is the angle in radians.
[tex]\[
F_X = 177 \cos(1.4835298641951802)
\][/tex]
4. Evaluate the cosine function and multiply by the force:
[tex]\[
F_X = 177 \times \cos(1.4835298641951802)
\][/tex]
5. Result:
The calculated x-component of the force is:
[tex]\[
\overrightarrow{F_X} = 15.42656646633549 \text{ N}
\][/tex]
Thus, the x-component of the force acting on the block is approximately [tex]\( 15.43 \text{ N} \)[/tex].
