Tipping a box against obstruction · CAP 2004 #Q14
Physics · mechanics
Problem
A uniform cubical box of mass rests on a horizontal floor with one edge against a small obstruction fixed to the floor. Can a horizontal force of magnitude applied on the box at the centre of the side opposite the obstruction tip the box? (a) No, never; (b) yes, only if ; (c) yes, is sufficient; (d) yes, only if .Intuitive explanation
The key is recognizing that tipping happens when the box rotates about the obstruction edge, not when the applied force simply overcomes friction. You need to compare torques around that pivot point: the tipping torque from force applied at the box's center versus the restoring torque from gravity acting at the center of mass. The box tips when the gravitational restoring torque can no longer balance the applied force's torque—find the critical force threshold by setting these equal.
Intuitive explanation
The key is recognizing that tipping happens when the box rotates about the obstruction edge, not when the applied force simply overcomes friction. You need to compare torques around that pivot point: the tipping torque from force applied at the box's center versus the restoring torque from gravity acting at the center of mass. The box tips when the gravitational restoring torque can no longer balance the applied force's torque—find the critical force threshold by setting these equal.