Explain a situation when the normal force is not equal to the force of gravity

Roller Coasters would be a situation when the normal force is not equal to the force of gravity.The only forces acting on the rider are the upward normal force n exerted by the car and the downward force of gravity w, the rider's weight.

What do you mean by "the normal force"?

The force perpendicular to a surface? If you press on an object, it exerts a force on the surface below that exceeds the weight of the object.

On an inclined plane, the Fn is only = to the y component of the Fg or vice versa.

In my opinion, this is a poorly worded question. My answer is: Any object sitting on a flat surface.

The question involves forces, which are vectors, which have direction as well as magnitude. So for my object, the normal force points straight up, the force of gravity points straight down. These two vectors, pointing in opposite directions, can never be equal (unless they're both zero vectors).
I'm sure the writer of the problem meant to say, "...magnitude of the normal force is not equal to the magnitude of the force of gravity."

In physics, the normal force is the force exerted by a surface to support the weight of an object resting on it. It acts perpendicular to the surface and prevents the object from sinking into or falling through it. Usually, when an object is at rest on a horizontal surface, the normal force is equal in magnitude but opposite in direction to the force of gravity acting on the object.

However, there are situations when the normal force is not equal to the force of gravity. Let's consider a few examples:

1. Inclined Plane: When an object is placed on an inclined plane, the normal force is not equal to the force of gravity. The force of gravity always acts vertically downwards, but the normal force acts perpendicular to the inclined surface. Since the surface is angled, the normal force is lesser than the force of gravity. The normal force can be calculated using the formula N = m * g * cos(theta), where m is the mass of the object, g is the acceleration due to gravity, and theta is the angle of the inclined plane.

2. Elevator: Consider standing on a scale inside an elevator. When the elevator is stationary or moving at a constant velocity, the normal force equals the force of gravity. However, when the elevator accelerates upwards or downwards, the normal force may differ from the force of gravity. If the elevator accelerates upwards, the normal force will be greater as it works against the force of gravity. Conversely, if the elevator accelerates downwards, the normal force will be lower as it works with the force of gravity.

3. Hanging Object: Another example is when an object is hanging from a ceiling or a support. In this case, the normal force is zero because it does not support the object vertically. The weight of the object is balanced entirely by the tension in the rope/chain supporting it.

It is essential to understand the forces acting on an object and their directions to determine if the normal force is equal to or different from the force of gravity in a given situation. Formulas and equations specific to the scenario can be used to calculate these forces precisely.