Does mass affect how likely an object is to topple over?

Question

I was at work recently pulling around some pallets when I had a thought. I wanted to know if the mass of the pallet had any influence on how likely it is for the pallet to topple over when going around a corner. I'm assuming that their shape, size, centre of mass etc is the same, as well as moving at the same speed and around the same corner.

I approached this from looking at it from the frame of the pallet and accounted for the centrifugal force (fake gravity acting horizontally) and the real gravitational force acting down, both through their centre of mass of course. I figured that so long as the resulting vector doesn't point beyond the pivot point then it won't topple, just like with a stationary object that is being tilted.

So all my reasoning tells me that the mass is irrelevant and both should be equally likely start toppling. When I try to test this though my prediction is shown to be false. I tried placing two identical objects with different masses onto an incline and gradually tilted them together to see if they started to topple together and I found that in every case (using different sets of two objects such as one empty bottle and one full bottle of the same shape, size etc) the lighter object always tipped over first. In fact I always had to tip the heavier object considerably more in order to get it to tip over. So is my reasoning just wrong or is there some other reason why my experiment disagrees with me?

Also even if they are equally likely to start toppling together, will one topple faster?

Answer 1

Your object will fall over whenever the torque due to gravity about the contact point with the ground is such that it rotates the object towards falling down.

What this means is that if the COM moves past a certain point, the object falls down. In your experiments this can be found by drawing a line vertically downward from the center of mass. If the line exits the body before reaching the incline, then the body will fall over. The higher the COM, the easier it is for this to happen. Therefore, the total mass does not matter, but how the mass is distributed does matter.

I tried placing two identical objects with different masses onto an incline and gradually tilted them together to see if they started to topple together and I found that in every case (using different sets of two objects such as one empty bottle and one full bottle of the same shape, size etc) the lighter object always tipped over first.

It is most likely the case that the empty bottle has a higher center of mass than the full bottle. This is why it falls over first. Also as a side note, a centrifugal force most likely does not come into play here. Especially if you are lifting your incline slowly enough as to not disturb the objects.

Answer 2

I found that in every case (using different sets of two objects such as one empty bottle and one full bottle of the same shape, size etc) the lighter object always tipped over first.

It is likely to be an experimental error.

For instance, let's consider a setup with empty and full bottles.

If the bottles are made out of light plastic, their shape could slightly change when they are filled, affecting their stability. The weight of the cap could make a difference. Slight vibrations will have a greater effect on an empty bottle.

If the bottles are made out of glass, there will be fewer factors in play and, therefore, the difference between empty and full bottles won't be as significant.

Also even if they are equally likely to start toppling together, will one topple faster?

If we neglect air resistance and assume no slippage and identical shape and weight distribution, they should topple at the same speed.