Center of mass on inclined plane

[Elbobo]

Homework Statement

A box with its center of mass off-center as
indicated by the dot is placed on an inclined
plane.

In which orientation does the box tip over?

Homework Equations

Teacher didn't even mention anything related to this

The Attempt at a Solution

Since the CM was at the top, the CG in this case was at the top. Gravity pulls straight downward and nothing is there to support the CM, so it would tip over in option 1, right?

 

[Doc Al]

Exactly. In order to not tip over, the center of mass must be over the base.

 

[thomate1]

I would like to clarify that the orientation of the box tipping over on an inclined plane depends on the distribution of mass within the box and the angle of the incline. The center of mass (CM) is the point at which the entire mass of the object can be considered to be concentrated, and it is the point where the gravitational force acts on the object. In this scenario, the location of the CM will determine the stability of the box on the inclined plane.

If the CM is located above the point of contact between the box and the plane, the box will tip over in the direction of the lower end of the incline. This is because the gravitational force acting on the box will create a torque that causes it to rotate in that direction.

However, if the CM is located directly above the point of contact between the box and the plane, the box will remain stable and will not tip over. This is because the gravitational force acting on the box will create a torque that is balanced by the normal force from the plane, resulting in no net torque and thus no rotation.

Therefore, without knowing the specific distribution of mass within the box and the angle of the incline, it is not possible to determine the orientation in which the box will tip over. It is important to consider the concept of center of mass in analyzing the stability of objects on inclined planes.