IIT JEE , AIEEE Forum - Physics , Mechanics

sahilgupta_iit

What is the necessary condition make a cube topple (numericals point of view). Both for horizontal and incilned plane.

a_JOSHI

If a body is resting on a rough slope, it will be on the verge of toppling over when the weight of the body acts through the edge of the part of the body which is in contact with the slope.

Slope not steep enough for toppling to occur:

Object on verge of toppling:

Here the object will topple:

This is because, about the edge of the object, there is a net anti-clockwise moment (turning effect).

Remember, the weight acts through the centre of gravity of the object.

aditi_g

torque(mg) > torque (buoyant force)

or

torque(mg)<torque(bouyant force)

sahilgupta_iit

aditi, this is not for a case inside a fluid. please explain it.

aditi_g

i gave u the logic to be applied whn a block is floating in a liquid...

sahilgupta_iit

what if when the block is resting on an incilned or forrce is applied on a block kept on horizontal surface? please explain.
and is the torque about the point about which it is toppling?

oneyeartogo

This ocuurs when the normal reaction offered by the floor shifts out of the body.

Normally the normal reaction acts on the centre of mass of body. When a force is applied on the top of the cube and the body doesn't topple. This happens because the normal reaction has shifted and now the torque due to it is equal to the torque due to external force. But if normal shifts out of the body, the body topples.

Hope u understood it. For any clarifications nudge me.

oneyeartogo

Consider a cube of edge length a kept on a flat surface (for simplicity sake). A force is applied of magnitude f is appplied on the cube at a ht. a from the ground & parallel to the ground. This force tries to make the cube translate as well as rotate about its centre, but we see that the cube rotates when we apply a force greater than or equal to a certain amt. of force.

When we apply a small force on the cube at a ht a from the ground and parallel to the ground, the torque of the force is F. a/2 in the clockwise sense ,but the body doesn't rotate, because this torque is equal in magnitude but opposite in direction to the torque generated by the normal reaction.

For a better explanation please refer to Resnick Halliday. It is explained very well in that.

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