Final answer:
The weight of an object on an inclined plane is decomposed into parallel and perpendicular components relative to the plane, calculated using trigonometric functions based on the angle of incline.
Step-by-step explanation:
When a set of cylinders are placed upon an inclined plane, the weight of each cylinder can be resolved into two components due to the angle of inclination. The components of the weight are the parallel component W|| and the perpendicular component W₁. The parallel component, which causes the object to accelerate down the slope, is calculated using W|| = W sin(θ) or W|| = mg sin(θ) where θ is the angle of inclination and m is the mass of the object.
Similarly, the perpendicular component, which is equal and opposite to the normal force exerted by the plane on the object, is calculated using W₁ = W cos(θ) or W₁ = mg cos(θ). To visualize these components, a right triangle can be drawn with the weight vectors, where the angle between the weight (W) and the perpendicular component (W₁) is the same as the angle of inclination. Using trigonometry, one can determine the magnitudes of the weight components rather than memorizing the formulas.