# Tipping of a cabinet and determining velocity at a given point?

• StephenHaw
In summary, the conversation discusses the calculation of whether a cabinet, when subjected to a force on its upper edge, will gain enough momentum to continue over the balance point and fall over or if the opposing moment due to mass and gravity will counter the momentum and return the cabinet to its base. It is determined that the work done by a force is the inner product of the force and displacement, and the work done by gravity on a body is directly related to the vertical displacement of its center of mass. The discussion also suggests calculating the increased gravitational potential energy at the tipping point and using minimal kinetic energy to calculate the work needed by an external force to topple the object.
StephenHaw
TL;DR Summary
A question on tipping, a cabinet is subject to a force greater than the tipping force to an angle of 10 degrees when the applied force is removed, how do I determine if momentum will cause the cabinet to fall over or fall back?
I am trying to determine if there is a set of formula to calculate if a cabinet will when subjected to a force on it's upper edge for an angular distance (not a duration) will gain enough momentum to continue over the balance point and fall over or whether the opposing moment due to mass and gravity will counter the momentum and return the cabinet to it's base.

I already know that for a turning moment that if F1D1 = F2D2 at the point at which tipping will begin: So a cabinet that is 1m tall, 0.5m wide and weight 60kg on a non slip floor would need just over 60*9.81*0.25/1 = 147.15 N to begin to move when the load is applied at the top edge of the cabinet.
The angle at which the CofG is to the pivot edge from the vertical plane is from trig tan-1 (0.25/0.5) = 26.56 degrees

However if a test required a 200N applied force on the cabinet we would know the difference in the applied turning moment would be 52.85N
causing the cabinet to tip. The force of 200N is constant and applied until the cabinet has tipped 10 degrees at which point the applied force is removed.

Now what I am trying to work out is how much K.E. is obtained by the cabinet at the point where the force is removed to understand its velocity to then work out how much further the cabinet will travel before either falling back onto its base or carrying on beyond the pivot point
and fall over.

In this respect perhaps I might be over thinking the problem, as I consider the turning moment applied by gravity is reducing as it approaches the balance point so the value for acceleration increases due to the increasing difference in the applied force and its opposing turning moment due to gravity.
The method to solve this I could then apply to different cabinets of different heights, widths and mass.
Any advice will be greatly appreciated.

The work done by a force is the inner product of the force and displacement. The work done by gravity on a body is directly related to the vertical displacement of its centre of mass.

If I imagine your scenario correctly, you could calculate the increased gravitational PE at the tipping point, and assuming minimal KE at that point, calculate the work needed by an external force to topple the object.

PeroK said:
The work done by a force is the inner product of the force and displacement. The work done by gravity on a body is directly related to the vertical displacement of its centre of mass.

If I imagine your scenario correctly, you could calculate the increased gravitational PE at the tipping point, and assuming minimal KE at that point, calculate the work needed by an external force to topple the object.
Thanks for the reply and it gives me a new perspective on the problem in terms of work and energy to see if there is a methodology there that I can apply.

## 1. What is the tipping point of a cabinet?

The tipping point of a cabinet is the point at which the cabinet begins to tip over due to an external force acting on it.

## 2. How is the tipping point of a cabinet determined?

The tipping point of a cabinet can be determined by calculating the center of mass of the cabinet and determining when it reaches a critical angle where the center of mass is no longer supported by the base of the cabinet.

## 3. What factors affect the tipping point of a cabinet?

The tipping point of a cabinet can be affected by the weight and distribution of items inside the cabinet, the material and design of the cabinet, and the surface on which the cabinet is placed.

## 4. How is the velocity at a given point on a tipping cabinet calculated?

The velocity at a given point on a tipping cabinet can be calculated using the conservation of energy principle, where the potential energy at the tipping point is converted into kinetic energy at the given point.

## 5. Why is it important to determine the tipping point and velocity of a cabinet?

Knowing the tipping point and velocity of a cabinet is important for safety purposes, as it can help prevent accidents and injuries. It can also be useful in designing and constructing cabinets to ensure they are stable and can withstand external forces.

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