Overview
The lecture introduces solving physics problems involving inclines (ramps) by adopting a tilted coordinate system aligned with the surface of the incline.
Inclines and the Tilted Coordinate System
- Problems involving inclines are best solved using a coordinate system aligned with the incline.
- Redefine the x-axis to be parallel to the incline, with positive x going down the incline and negative x going up.
- Redefine the y-axis to be perpendicular to the incline, with positive y pointing away from the surface, negative y into the surface.
- This new system differs from the standard horizontal x and vertical y axes.
Forces on an Incline
- The normal force (fn) always acts perpendicular and away from the incline surface (y-direction in new system).
- Weight (gravity) always acts vertically downward, not aligned with the new x or y axes.
- Weight must be split into two components: one parallel to the incline (x-direction), one perpendicular (y-direction).
Components of Weight on an Incline
- The parallel (x) component of weight: ( w_{x} = w \sin{\theta} ), where θ is the incline angle; positive x is down the ramp.
- The perpendicular (y) component of weight: ( w_{y} = -w \cos{\theta} ); negative y points into the incline.
- The angle θ in these equations is the same as the incline angle.
Key Terms & Definitions
- Incline (Ramp) — A surface tilted at an angle from the horizontal.
- Normal force (fn) — The force perpendicular to a surface, here perpendicular to the incline.
- Weight components — The force of gravity split into parts parallel and perpendicular to the inclined surface.
- Inclination angle (θ) — The angle between the incline and the horizontal ground.
Action Items / Next Steps
- Review the example problem on inclines that will be covered in the next lecture.
- Practice decomposing forces on an incline using the new coordinate system.