Not homework, but question about pushing over a heavy slab at rest

[wildside50]

Homework Statement

So the concept is, you've got a very large slab of stone. For arguments sake, let's say it's about 8 feet high, 4 feet across, and 2 feet thick. How much force would it take to push the slab over, pushing at the top for maximum torque. If granite weighs about 165 lbs/cubic ft, would a human be able to push this object over? How about if it was only 1 foot thick, or 6" thick?

Homework Equations

The Attempt at a Solution

I tried some things using torque but I think I was way off. I took one of the bottom edges as the point of rotation and using the thickness of the slab as the radius, and multiplying by the force of gravity, I got a torque, namely 9.8m/s * 4800 kg * .6 m, and used that resulting torque as the required torque to oppose gravity and rotate the object about that edge. That resulted in a very large # of 28224 N*m. This torque I then set equal to the unknown force time the height of slab (the new rotational edge) getting F = 28224 N*m / 2.4 m = 11760 N. That seems huge. That means even if the object were 100 feet tall and still weighed the same, it would take 940 N of force to tip it. Or if the base was 6" instead of 2', it would still take 2987 N. That still seems like a big number, as in my mind a 100 ft tall object with a 2 ft base would be highly unstable. Am I taking a completely wrong approach to sovling this or are those #'s right?

 

[Mindscrape]

Another thing to keep in mind is that there will be a point of thickness will be too great, and the object will simply slide rather than tip over. Additionally, as you have noted, the less thickness there is the easier it will be to push the slab over, which is due to less mass and less points of contact for frictional effects opposing you pushing the slab over.

Here are things at work:
1) The mass of the object. It is easier to push a less massive object than a more massive object. Granite is very dense and will become to massive for a human pretty quick. Imagine the opposite scenario, of say paper, and the dimensional effects are easy to visualize.
2) The lever arm height. "Give me a lever long enough and I will move the world." (Or something like that.) The further away from the pivot you can push, the more torque you will get.

I don't really want to work out the numbers, but 8 feet high will give a pretty good lever arm compared to the two feet of thickness. I think it is possible for a human to be able to do it.

 

[m2003]

I would approach this problem by first considering the physical properties and characteristics of the slab. The dimensions and weight of the slab are important factors in determining the force required to push it over. However, the shape and distribution of mass within the slab also play a role in its stability and resistance to being pushed over.

To accurately determine the force required, I would need to know the exact dimensions and weight of the slab, as well as its center of mass and any potential weak points or irregularities in its shape. I would also consider the surface on which the slab is resting, as a smooth surface may require more force to overcome friction.

In terms of the calculations, I would use principles of statics and mechanics to analyze the forces and torques acting on the slab. This would involve breaking down the slab into smaller components and considering the forces and torques acting on each component. I would also need to take into account the direction and location of the applied force, as well as any external forces acting on the slab (such as wind or vibrations).

In short, the force required to push over a heavy slab at rest is a complex and multi-faceted problem that cannot be accurately solved without a thorough analysis of the physical properties and forces acting on the slab. It is not simply a matter of using a formula or calculating torque. I would need to carefully consider all factors and use appropriate methods to arrive at an accurate solution.