I'm having a hard time with some free body diagrams. If you have a box on a slope/ramp and the angle of the ramp is X degrees why is it that the angle between the normal force and the gravitational force is also X degrees? Am I missing something obvious here?
Normal means perpendicular to the slope. The slope is at X deg to the horizontal, and the normal is 90 deg to that, so to the horizontal, the normal then is 90+x, but measuring the normal to the perpendicular, you subtract 90, so the normal is to vertical is X deg. gravity is vertical.
Yes, geometry. Sketch it carefully.
Think about what happens to the angle between straight down and the normal from the object to the ramp as the slope increases from zero. At zero you see the normal to the ramp (level road in this case) is straight down like gravity. As the slope goes up, the normal goes up, but gravity remains straight down.
You guys are great! Now I get it!
When analyzing problems involving inclined planes or ramps, it's important to consider the forces acting on the object to understand its motion. One of the key forces to consider is the gravitational force, which always acts vertically downward towards the center of the Earth.
On an inclined plane, the gravitational force can be decomposed into two components: one parallel to the plane (F_parallel) and one perpendicular to the plane (F_perpendicular). The angle between the incline and the vertical direction is denoted as X degrees.
Now, let's consider the normal force (F_normal) acting on the object. The normal force is always perpendicular to the surface of contact, which in this case is the inclined plane. Since the inclined plane itself is at an angle X degrees with respect to the vertical direction, the normal force will also be perpendicular to the inclined plane.
By definition, when two lines are perpendicular to each other, the angle between them is always 90 degrees. Therefore, the angle between the normal force and the gravitational force is X degrees in this case, as both forces are perpendicular to the inclined plane.
To summarize, the angle between the normal force and the gravitational force is X degrees because both forces are perpendicular to the inclined plane, which is inclined at an angle of X degrees with respect to the vertical direction.