The "downward" on the "curved surface" is a 3D model to explain and visualize the effect.
The force of gravity causes a teardrop to roll down your cheek. Gravity pulls the teardrop downwards towards the Earth's surface, causing it to slide down your cheek due to the slope and curvature of your skin.
Gravity is the force that pulls downwards on a rocket as it is launched into space. Gravity acts to pull the rocket back towards the Earth's surface.
Gravity is responsible for stopping the downward flow of water. As water flows downwards due to gravity, it eventually reaches a point where the force of gravity pulling it downward is balanced by other forces such as friction and surface tension, which prevent the water from continuing to flow downwards.
The radius of curvature is the distance from the center of a curved surface or lens to a point on the surface, while the center of curvature is the point at the center of the sphere of which the curved surface is a part. In other words, the radius of curvature is the length of the line segment from the center to the surface, while the center of curvature is the actual point.
A static object does not move downwards because the force of gravity acting on it is equal and opposite to the normal force exerted by the surface it rests on. This results in a state of equilibrium where the net force on the object is zero, preventing it from moving downwards.
The stomach has a greater and lesser curvature. The greater curvature is the more lateral of the two.
In general, liquids have a flat surface, because gravity tends to flatten them out. It is not perfectly flat, and often has waves or ripples if something has disturbed it. Even a perfectly undisturbed liquid is not perfectly flat, since gravity pulls in the direction of the center of the Earth, and there will be some curvature in the surface as a result - but since the center of the Earth is very distant, the curvature is slight. An additional influence on the shape of the surface of a liquid is surface tension. Water, in particular, has an attraction for many substances, and will rise up slightly where it meets the walls of its container.
Two forces acting on a book are gravity pulling it downwards towards the Earth and the normal force exerted by the surface it is resting on that pushes back against gravity to keep the book stationary.
When water soaks into the soil, it is referred to as infiltration. This is the process where water enters the soil surface and moves downwards due to the force of gravity.
In each point, there is a line. The curvature of the surface in this direction is zero. Therefore the maximum curvature is positive and the minimum is negative. Gauss curvature in this point is the product of this max and min, and therefore is negative (or zero).
Yes, gravity acts on marbles just like it does on all objects with mass. The force of gravity pulls the marble towards the center of the Earth, causing it to fall when dropped or roll downwards on an inclined surface.
The radius of curvature is important in physics because it determines the curvature of a wavefront or a mirror or lens surface. In the case of light or other waves, the radius of curvature affects how the waves are focused or dispersed. A smaller radius of curvature results in a more curved surface, which can focus light or waves to a point, while a larger radius of curvature leads to a flatter surface that disperses the waves.