Calculating the force required to topple an object?

  • Context: Undergrad 
  • Thread starter Thread starter paulw99
  • Start date Start date
  • Tags Tags
    Force
Click For Summary

Discussion Overview

The discussion revolves around calculating the force required to topple an object, specifically focusing on the dynamics involved in pushing or lifting an object to the point of overturning. Participants explore various factors influencing this force, including the object's dimensions, material properties, and the surface it rests on.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested
  • Mathematical reasoning

Main Points Raised

  • One participant inquires about a formula for calculating the force needed to topple an object, providing details about the object's dimensions and material.
  • Another participant questions the inquirer's knowledge of rotational dynamics, suggesting that understanding this concept is crucial for the discussion.
  • A participant explains that there is no simple equation applicable to all situations, using the example of a large cube-shaped rock to illustrate how the force required to lift and topple it can vary significantly based on conditions.
  • It is noted that the force required to initially lift an edge of the object is easier to calculate than the force needed to topple it once it is balanced.
  • The complexity of the situation increases if the object is lifted quickly, such as with an explosive force, raising questions about whether the object will continue to rotate or fall back down.
  • Another participant emphasizes the importance of considering friction between the object and the ground, as it affects whether the object will topple or slide when a horizontal force is applied.
  • A later reply reiterates the need to consider the center of mass and the conditions under which the object will overbalance, suggesting that a small additional force can cause it to topple once the center of mass is directly above the pivot point.
  • One participant provides a mathematical approach, detailing the relationship between the weight of the object, the applied force, and the moments about the pivot edge, indicating that the force required to topple the object can be calculated based on these factors.

Areas of Agreement / Disagreement

Participants express various viewpoints on the complexity of calculating the force required to topple an object, with no consensus reached on a single formula or method. The discussion includes multiple competing perspectives on the factors that influence the toppling force.

Contextual Notes

Participants highlight limitations in the discussion, such as the dependence on specific conditions like surface type and the dynamics of force application, which remain unresolved.

paulw99
Messages
2
Reaction score
0
Is there a formula that calculates the force required to "push over" or topple an object? I know all the details of the object (length, width, height, material, etc) and the object will be resting on a flat surface. If anyone can point me in the right direction I'd be very grateful.

Note: This is not a homework/school related question.
 
Physics news on Phys.org
How much do you know about rotational dynamics?
 
Shyan said:
How much do you know about rotational dynamics?
Nothing.
 
There isn't a simple equation that covers every situation.

Consider a huge rock in the shape of a cube 10m x 10m x 10m. It would take a considerable force to lift one side just 1 mm off the ground... but once you have lifted it to the point where it's balanced on an edge the force required to topple it over could be very small. The weight of a small dust particle landing on one side might be enough to topple it. In practice it would depend on what the rock was resting on. If it was on soft ground it might sink in and be quite difficult to topple. If it was on a hard surface it might be easy. Which force did you want to know, the initial force required to lift an edge or the final force required to topple it? The initial force is reasonably easy to calculate. It's also reasonably easy to calculate the force needed to lift it at any angle in between.

The above assumes you are lifting it slowly. The situation gets more complicated if you lift the edge of an object quickly. For example suppose you put some explosive under one edge. An explosion would apply a force for a very short period of time. It might only be 1/10th of a second but it might be long enough to get the thing rotating at some velocity about the opposite edge. The question then becomes will it keep rotating or slow, stop and fall back down? As the block rotates the centre of mass rises and that takes energy (=mgh). If you know the initial velocity you might be able to calculate if the explosion gave the block enough energy to lift the centre of mass to the point where it would continue to topple over. If not, then it would fail to reach that height and fall back down.
 
PS: If the force is limited to a horizontal push on the side of the object then you need to know about the friction between the object and the ground. For example will it topple over or just slide along the ground? In the real world it's not always easy to be sure what will happen because the friction changes as the object is lifted. eg It might start to topple, then as friction reduces it might start to slide and fall back down. Things get easier if the object is up against a step or similar that stops it sliding.
 
paulw99 said:
Is there a formula that calculates the force required to "push over" or topple an object? I know all the details of the object (length, width, height, material, etc) and the object will be resting on a flat surface. If anyone can point me in the right direction I'd be very grateful.
Generally, you need to look at tilting the object so that its centre of mass moves to be directly above the supporting edge the block is rotating about.Then the tiniest extra force is enough to make it overbalance---and it obligingly completes the rotation by itself (with the assistance of gravity).
 
  • Like
Likes   Reactions: Mayank Pathak
Consider a cubic object of size L x B x H and density 'D'. Weight of the object W=LxBxHxD. Since the object is assumed to be homogenous, the Centre of Gravity will be at the centre with co-ordinates from one of the edges as L/2, B/2 and H/2. The minimum force to topple it will be when the force is applied on the top edge horizontally when you are looking on the side containing the smaller base of B. The object will tend to topple about the diagonally opposite edge. The stabilising effect due to the weight of the object about this edge will be WxB/2 and the destabilising moment due to applied force F will be FxH. When (FxH) exceeds (WxB/2), the object will start to topple. The actual force at th time of toppling will be less since the moment arms change during the toppling process.
 

Similar threads

Undergrad Not a physics major -- Question about how far we can kick an object
  • · Replies 22 ·
Replies
22
Views
2K
High School Force required to stretch training resistance bands
  • · Replies 12 ·
Replies
12
Views
3K
Undergrad Rail gun - point of application of force?
  • · Replies 21 ·
Replies
21
Views
2K
Undergrad What is the minimum force required to lift an object?
  • · Replies 128 ·
5
Replies
128
Views
12K
Undergrad The time for a tilted brick to hit the ground
  • · Replies 16 ·
Replies
16
Views
3K
Undergrad Normal force and details of the Earth holding up an object
  • · Replies 12 ·
Replies
12
Views
2K
Undergrad Distributed Forces and force density....
  • · Replies 8 ·
Replies
8
Views
3K
Undergrad Question about Momentum vs. Kinetic Energy vs. Deforming In Collisions
  • · Replies 2 ·
Replies
2
Views
2K
Undergrad How to calculate the angle at which a cylinder topples?
  • · Replies 3 ·
Replies
3
Views
4K
High School Questions about momentum and force as well as normal force/friction
  • · Replies 35 ·
2
Replies
35
Views
5K