Activityl A block on an incline plane is subjected to a poice due to gravity \( \overrightarrow{\mathrm{F} g} \) of 287 N straight down, if thecomponat of the gravitational force parallel to the siope is \( \overrightarrow{\text { Fgx }}=123 \), 7 N in the Hegative \( x \) direction (down the slope), what is the incline of the siope.

To find the incline of the slope, we can use the relationship between the gravitational force \( F_g \) and its components. The gravitational force acting straight down can be resolved into two components: one parallel to the slope and one perpendicular to it. We know the parallel component \( F_{gx} = 123.7 \, \text{N} \). Using the formula: \[ F_{gx} = F_g \cdot \sin(\theta) \] we can rearrange it to find \( \theta \): \[ \theta = \arcsin\left(\frac{F_{gx}}{F_g}\right) = \arcsin\left(\frac{123.7}{287}\right) \] Calculating this gives: \[ \theta = \arcsin(0.431) \approx 25.6^\circ \] So, the incline of the slope is approximately \( 25.6^\circ \). --- Did you know that inclined planes were a key part of ancient engineering? The Egyptians used ramps to construct the Pyramids of Giza, showing that leveraging angles can help in lifting heavy loads! These simple machines paved the way for more complex tools, embodying the principle of mechanical advantage. In real-world applications, inclined planes can be found everywhere: from wheelchair ramps providing accessibility to loading docks, and even in amusement park rides demonstrating thrilling drops. Understanding the physics behind these slopes not only helps us design safer structures but also enhances our daily conveniences.