Force required to tip an object

[some4544]

So I need to find equations for the force required to tip over a cylindrical object. This is fairly straight forward in the case when the force is applied above the centre of mass, by taking moments about the pivot corner. However, in the case where the force is applied below the centre of mass so that the object falls towards where the force was applied, I understand that the pivot corner has to 'slide' so that it is underneath the centre of mass, but I am struggling to quantify this in an equation.

Any help would be greatly appreciated

 

[PeroK]

So I need to find equations for the force required to tip over a cylindrical object. This is fairly straight forward in the case when the force is applied above the centre of mass, by taking moments about the pivot corner. However, in the case where the force is applied below the centre of mass so that the object falls towards where the force was applied, I understand that the pivot corner has to 'slide' so that it is underneath the centre of mass, but I am struggling to quantify this in an equation.

Any help would be greatly appreciated

You need to do some experiments to test your theory. I would say that a torque is a torque and the COM is not a critical point in this respect.

 

[some4544]

You need to do some experiments to test your theory. I would say that a torque is a torque and the COM is not a critical point in this respect.

Hi, thank you for responding

The reason I'm actually asking this is for a student I'm tutoring who has carried out this experiment, we're now just trying to find a theory to put in the lab report so that it can be written up in a logical manner with some sort of hypothesis. The student conducted the experiment by varying the height of the centre of mass, and using a force meter to measure the minimum force required to tip the object (the height at which the force was applied was kept constant, as was mass etc). The results showed a (roughly) linear increase in force required when the height of the centre of mass was increased up to the height at which the force was applied, and then a (roughly) linear decrease.

When I first saw this problem, I agreed with you, and thought the height of the centre of mass would not affect the force required because the torque is independent of this before the object tips by a small angle, which is why I'm struggling to put some equations together. I have managed to kind of fudge something in the case that the object falls away from the point of application of force by assuming the object has already tipped by a small angle, but am struggling to do the same when it falls towards the point of application of force.

Any thoughts on how to model this would be great!

 

[PeroK]

Hi, thank you for responding

The reason I'm actually asking this is for a student I'm tutoring who has carried out this experiment, we're now just trying to find a theory to put in the lab report so that it can be written up in a logical manner with some sort of hypothesis. The student conducted the experiment by varying the height of the centre of mass, and using a force meter to measure the minimum force required to tip the object (the height at which the force was applied was kept constant, as was mass etc). The results showed a (roughly) linear increase in force required when the height of the centre of mass was increased up to the height at which the force was applied, and then a (roughly) linear decrease.

When I first saw this problem, I agreed with you, and thought the height of the centre of mass would not affect the force required because the torque is independent of this before the object tips by a small angle, which is why I'm struggling to put some equations together. I have managed to kind of fudge something in the case that the object falls away from the point of application of force by assuming the object has already tipped by a small angle, but am struggling to do the same when it falls towards the point of application of force.

Any thoughts on how to model this would be great!

If the pivot point is not fixed, then the cylinder accelerates and may rotate in the opposite direction. One factor, therefore, is the static/kinetic friction with the floor.

 

[PeroK]

PS You need to be careful. If the applied force is slightly upwards, then that may take the frictional force out of the equation, which means that it might be difficult to model the motion accurately.

 

[some4544]

PS You need to be careful. If the applied force is slightly upwards, then that may take the frictional force out of the equation, which means that it might be difficult to model the motion accurately.

This is what I'm concerned about - the experiment has already been conducted but it's proving really quite tricky to model this, I think partly as well because there's no obvious pivot point that remains stationary.

Any thoughts on how to overcome this would be most welcome!

 

[PeroK]

This is what I'm concerned about - the experiment has already been conducted but it's proving really quite tricky to model this, I think partly as well because there's no obvious pivot point that remains stationary.

Any thoughts on how to overcome this would be most welcome!

Logically you have:

1) As long as the pivot point does not move, you have a minimum force required.

2) When this force reaches the maximum static friction, you have a critical point.

3) The simplest model is a constant force of kinetic friction. Should be less than the static friction.

4) In this model, you could consider moments about the COM. You need to account for your accelerating reference frame, but this should not affect moments about the COM.

 

[jrmichler]

This is fairly straight forward in the case when the force is applied above the centre of mass, by taking moments about the pivot corner. However, in the case where the force is applied below the centre of mass so that the object falls towards where the force was applied

You have two possible cases:
1) Slowly increase the force until the cylinder either slides or tips. A free body diagram is a big help to understand why it does not matter if the point of application of the force is above, below, or in line with the COM. A proper FBD will also show why the height of the COM does not matter.
2) Suddenly apply a large force. In that case, the FBD has an additional force due to acceleration. Then it does matter where the point of application is relative to the COM. A FBD will help to understand this case.

 

[tech99]

So I need to find equations for the force required to tip over a cylindrical object. This is fairly straight forward in the case when the force is applied above the centre of mass, by taking moments about the pivot corner. However, in the case where the force is applied below the centre of mass so that the object falls towards where the force was applied, I understand that the pivot corner has to 'slide' so that it is underneath the centre of mass, but I am struggling to quantify this in an equation.
Any help would be greatly appreciated

I am sure you can deal with the problem of overturning using statics. However, if the cylinder starts to tilt, the force will push it right over, because the restoring moment arm reduces. Frictional resistance will be the same whether resting on the flat face or on the edge. This is because friction is independent of contact area and the downward force is unaltered. So the possibility of tilting then slipping does not seem likely. Further, the cylinder cannot fall towards the force, as this requires the centre of mass to move towards the applied force and is contrary to Newton. I would agree that the cylinder has stored PE, which might allow that, but our force cannot begin to raise the cylinder about its near edge without moving the centre of mass towards itself. This can only happen if our force is applied as an impulse rather than a steady force. In such a case, the inertia of the cylinder comes into play and we have to deal with it as a rotational impulse together with the moment of inertia.