In a coordinate system where the $x$-axis is aligned along an inclined plane and the $y$-axis is perpendicular to the plane, which of the following forces always lie along the coordinate axes for an object resting on the plane?

• A. The normal force and the friction force
• B. The friction force and the total gravitational force
• C. The normal force and the component of gravity perpendicular to the plane
• D. The applied force and the component of gravity parallel to the plane

Answer: (C)

Verified step by step guidance

1. Step 1: Understand the coordinate system setup. The x-axis is aligned along the inclined plane (parallel to the surface), and the y-axis is perpendicular to the inclined plane (normal to the surface). This means any force parallel to the plane lies along the x-axis, and any force perpendicular to the plane lies along the y-axis.
2. Step 2: Identify the forces acting on the object resting on the inclined plane. These typically include the gravitational force (weight), the normal force from the plane, and the frictional force if present.
3. Step 3: Analyze the direction of the normal force. The normal force is always perpendicular to the surface of contact, so it acts along the y-axis (perpendicular to the plane).
4. Step 4: Break down the gravitational force into components relative to the inclined plane. The weight vector can be decomposed into two components: one perpendicular to the plane (along the y-axis) and one parallel to the plane (along the x-axis).
5. Step 5: Consider the friction force direction. Friction acts parallel to the surface, so it lies along the x-axis. However, the friction force depends on the motion or tendency to move, so it is not always guaranteed to be present or aligned in a fixed direction without additional information.