Final answer:
To calculate the force of gravity acting downwards on an inclined plane, resolve the gravitational force into a parallel component using mg sin(θ) and a perpendicular component using mg cos(θ). The parallel component causes acceleration down the incline, while the perpendicular component balances the normal force.
Step-by-step explanation:
To calculate the force of gravity downwards on an inclined plane, you need to resolve the gravitational force into two components: the perpendicular component (w₁) and the parallel component (w₂). The component of gravity acting parallel to the plane often denoted as w₂ or W∥, is what causes the object to accelerate down the plane. This component can be calculated using the formula w₂ = mg sin(θ), where m is the mass of the object, g is the acceleration due to gravity, and θ is the angle of the incline.
On the other hand, the perpendicular component of the weight, w₁ or W₁, is equal in magnitude to the normal force (N) and can be determined using w₁ = mg cos(θ). This component does not contribute to the acceleration of the object down the plane.
The force of friction f, if present, acts in the opposite direction to w₂, and its magnitude is calculated as f = μ N, where μ is the coefficient of friction.