Can anyone Explain why a glass tips over when pushed from the top?

[linuxux]

Homework Statement

A glass has a height of 10 cm, and a diameter of 2 cm, it weight 300g and a coefficient of friction equal to .30 exists. Will it slip or tip?

Homework Equations

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The Attempt at a Solution

Im almost certain there are no calculations informed since i have been hard pressed to find equations relating height and friction. But i did test this theory my self on a glass and it did tip. Is the reason it tips because the farther away you are from the base, the more perpendicular is the applied force in respect to the base, because is you push from the bottom of the glass all the force is against the friction. Is this right?

 

[Doc Al]

Is the reason it tips because the farther away you are from the base, the more perpendicular is the applied force in respect to the base, because is you push from the bottom of the glass all the force is against the friction. Is this right?

It's certainly true that the higher up the force is applied, the more torque it exerts. Whether it tips or not depends on whether the applied torque is greater than the torque due to gravity.

Assume for the moment that the glass doesn't slip. What applied force is required to overcome gravity? Would a force of that magnitude be enough to overcome static friction?

 

[m2003]

Yes, your explanation is correct. When the glass is pushed from the top, the force is applied at a point farther away from the base, causing a larger moment arm and thus a larger torque. This torque causes the glass to tip over, as opposed to being pushed from the bottom where the force is directly opposing the friction and preventing it from slipping or tipping. Additionally, the shape of the glass, with a narrower base and wider top, also contributes to the tipping motion. The coefficient of friction also plays a role, as a higher coefficient would increase the resistance to slipping or tipping.