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Someone asked me this question and I am going to try to ask it as 'proper' as possible. Imagine there is a door and it needs a mass on the floor at the edge of the door to keep it from swinging shut. If I put one mass, it swings shut. However if I add another mass it stops the door from swinging shut. Why is that? I know it has to do with torque which is the cross product of the perpendicular force and distance. Does the increase in mass increase the force on the door and thus opposes the turning motion?

dreamin
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  • My best guess is that there are two effects: by increasing the overall weight of the door you increase the friction at the hinges, and you also increase the moment of inertia (since the mass is far from the hinge). Thus the door will need a far greater torque in order to swing shut. – G. Paily Oct 28 '14 at 15:28
  • Whoops, didn't realize that the mass was on the floor. SlySherZ has it right. – G. Paily Oct 28 '14 at 15:45
  • Torque is the *cross* product of the radius and the force, not the dot product – pho Oct 28 '14 at 16:16
  • related http://physics.stackexchange.com/questions/137682/distinction-between-torque-and-force – Nikos M. Oct 28 '14 at 17:06

2 Answers2

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The force by static friction that the ground does on the mass to prevent it from moving depends on the reaction force, which means more mass create greater opposition to movement. The force that the mass may apply on the door to prevent it from moving is limited by the previous one.

If you have a constant torque being applied on the door (the same logic applies if the torque changes over time, but it's never bigger than a threshold), you need a force to create a torque in the opposite direction to keep the equilibrium state, and this torque is higher with higher forces applied by the mass. It's also higher if the masses are closer to the edge of the door.

SlySherZ
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The question is not detailed enough, so I am going to make some assumptions: 1)the door is vertical and on hinges; 2)there is some force (wind?) pushing on the surface of the door, creating a torque that tends to close the door; 3)a small mass is placed on the floor to try to prevent the door from closing, but it fails; 4)the small mass is replaced with a larger one and the door does not close. "Why is that?"

The reason is that the larger mass produces a larger friction force which creates a torque large enough to counteract the torque being applied by the previous (wind) force, so the door does not move.

Guill
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