What is the component force of gravity pulling a mass down an inclined plane?

When a mass is placed on an inclined plane, gravity acts directly downwards, pulling the mass towards the center of the Earth. However, since the inclined plane is angled, only a component of this gravitational force actually acts to pull the mass down the slope of the incline.

To determine the component of gravitational force acting parallel to the slope (the force pulling the mass down the inclined plane), we can use trigonometric functions. The total gravitational force acting on the object is given by the product of its mass (m) and the acceleration due to gravity (g).

When decomposing this force vector into components relative to the incline, the force acting parallel to the incline is given by the sine of the angle of the incline (θ) because this angle describes the relationship between the gravitational force and its component along the slope. Specifically, the force acting parallel to the incline can be mathematically expressed as:

Force parallel to incline = mg × sin(θ)

This is why the correct expression for the component force of gravity pulling a mass down an inclined plane is represented by using the sine function with respect to the angle of the incline.

In contrast, the other options involve different calculations that either do not correctly account for the angle of the incline