Why does increasing an angle of incline increase the component of weight?

Increasing the angle of incline increases the component of weight because it increases the gravitational force acting parallel to the slope.

In physics, the weight of an object is the force exerted on it due to gravity. This force always acts vertically downwards. However, when an object is placed on an inclined plane, this weight can be resolved into two components: one acting perpendicular to the plane (the normal force) and one acting parallel to the plane (the component of weight). Understanding forces and motion is crucial in comprehending how this works.

The component of weight acting parallel to the plane is given by Wsinθ, where W is the weight of the object and θ is the angle of incline. As the angle of incline increases, the value of sinθ also increases (since the sine of an angle increases as the angle increases from 0 to 90 degrees). Therefore, the component of weight acting parallel to the plane also increases. The principle of Newton's first law further illustrates why an unbalanced force, such as the component of weight down an incline, results in motion.

This is why you feel heavier when you're walking up a steep hill compared to when you're walking on flat ground. The component of your weight acting parallel to the slope is greater, so you have to exert more force to overcome it. Additionally, the concept of energy types explains why moving up an incline requires more energy, correlating to the increase in the gravitational potential energy component of your weight.

In contrast, the component of weight acting perpendicular to the plane is given by Wcosθ. As the angle of incline increases, the value of cosθ decreases (since the cosine of an angle decreases as the angle increases from 0 to 90 degrees). Therefore, the component of weight acting perpendicular to the plane decreases as the angle of incline increases.

This is why objects seem lighter when you lift them straight up compared to when you slide them up an inclined plane. The component of their weight that you have to overcome is smaller when you lift them vertically. Understanding vectors in physics can help clarify how forces like weight are broken down into components.

IB Physics Tutor Summary: When the angle of an incline increases, the weight component acting down the slope increases because the sine value of the angle (used to calculate this component) grows as the angle gets larger. This makes objects feel heavier on steep inclines. Meanwhile, the weight component acting into the slope decreases as the angle grows, because the cosine value (used for this calculation) drops.