Tesla3
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#1
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Hi,
I can't understand the concept regarding sliding and toppling of an object at the same time. For example, if we have a box placed on an inclined plane and we slowly increase the angle of inclination. Also we know that the angle at which the box is about to slide is similar to the angle at which the box is about to topple. Can sliding and toppling occur at the same time? If yes, how is it possible? Is sliding related to distance travelled by the block? As the block will travel some distance due to the toppling. I have attached a diagram which shows the way I am thinking about this .Can someone please elaborate it for me. Thanks in advance.
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mqb2766
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Sliding would occur if the weight down the slope was greater than limiting friction.
Toppling (rotation) would occur if the x component of the com was to the right of B. The vertical weight would produce a moment about B.
You could select mu (coeff of friction) to coincide with the slope angle where the com is directly above B
Last edited by mqb2766; 9 months ago
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Tesla3
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#3
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(Original post by mqb2766)
Sliding would occur if the weight down the slope was greater than limiting friction.
Toppling (rotation) would occur if the x component of the com was to the right of B. The vertical weight would produce a moment about B.
You could select mu (coeff of friction) to coincide with the slope angle where the com is directly above B
Also is my diagram showing both sliding and toppling?
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mqb2766
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(Original post by Tesla3)
Also is my diagram showing both sliding and toppling?
To show toppling would occur, you'd need to mark the com to the right of B in the first picture and on the right, the net force (resolved weight - friction) on the object would be > 0. Not really sure how you're drawing that?

Note that when the com is above B and mu represents the slip angle (tan), the object would be in unstable equilibrium, similar to a support point.
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Tesla3
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(Original post by mqb2766)
To show toppling would occur, you'd need to mark the com to the right of B in the first picture and on the right, the net force (resolved weight - friction) on the object would be > 0. Not really sure how you're drawing that?
I get that.. ummm, After drawing those forces at right positions in first diagram, does second diagram concludes the final position in the right way?
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mqb2766
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(Original post by Tesla3)
I get that.. ummm, After drawing those forces at right positions in first diagram, does second diagram concludes the final position in the right way?
Looks good.
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Tesla3
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(Original post by mqb2766)
Looks good.
Also, I want to ask one more question. Does sliding means covering some distance or not? I think it does mean that.
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mqb2766
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(Original post by Tesla3)
Also, I want to ask one more question. Does sliding means covering some distance or not? I think it does mean that.
Yes. Can't see how you could slide but not cover distance.
Is there a specific question?
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Tesla3
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(Original post by mqb2766)
Yes. Can't see how you could slide but not cover distance.
Is there a specific question?
No, not any particular question perhaps. Although, I was just visualizing how sliding and toppling occurs at the same time. So I could say that when the box topples and is done toppling, it has covered some distance and therefore has gone through sliding as well.
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mqb2766
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(Original post by Tesla3)
No, not any particular question perhaps. Although, I was just visualizing how sliding and toppling occurs at the same time. So I could say that when the box topples and is done toppling, it has covered some distance and therefore has gone through sliding as well.
It would be rare to have such a question. Both would have to just past their limiting values. How small would that be? Also the friction on the body as it rotates about a point would be different from one side being in contact. Also, would you model the impact when the object hits the slope after rotating etc.

If you increased the plane slowly until toppling (just) occurred, the net force on the body to slude would be just greater than zero (very small).
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Tesla3
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(Original post by mqb2766)
It would be rare to have such a question. Both would have to just past their limiting values. How small would that be? Also the friction on the body as it rotates about a point would be different from one side being in contact. Also, would you model the impact when the object hits the slope after rotating etc.

If you increased the plane slowly until toppling (just) occurred, the net force on the body to slude would be just greater than zero (very small).
I see what you are trying to say. That makes sense.
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