Consider the block shown above supported by feet at A and B that is at rest on a rough floor. A horizontal force P is applied to the right on the block. As the magnitude of P is increased slowly, two things happen simultaneously:
- The normal force, NA, at foot A decreases as the normal force at foot B, NB, increases. Provided that the block does not slip first, the normal force at A will decrease to zero, meaning that a state of impending tipping exists.
- The total net friction force fA + fB increases. Provided that the block does not tip first, the friction forces at A and B will reach their maxima, meaning that a state of impending slipping exists.
QUESTION: Which happens first, tipping or slipping? The answer to that question depends on the height at which the force P is applied to the block and on the coefficients of static friction at the feet. We need to work out the problem two times in order to determine tipping or slipping: once assuming tipping and once assuming slipping.
Animation
Consider the animation from a simulation of this problem for this problem. On the left, the force P is applied low on the block, and on the right the force P is applied high on the block. The coefficients of static friction are the same for both cases. As we can see from the animation, the low-applied force slips before it tips, whereas for the high-applied force, the block tips first. Notice how the normal force at A decreases much more quickly for the high-applied case on the right than for the low-applied force on the left.
[Please note that the animation shows some oscillations back and forth in the friction forces. These oscillations will not be seen in the physical system. These are artifacts of the numerical integration method in the simulation.]
