Friction between two bodies (theoretical situation)

[limorgav]

What happens if we apply on B a force bigger than the static friction with the floor and also bigger than the static friction with the upper body A, but smaller than their sum? Will B move? what about A?

 

[HallsofIvy]

You are applying the force to B? Then, since the force is greater than the static friction between B and the floor, B will start to move. Once it has started to move, the problem reverts to "kinetic friction". The net force on B will be the total force minus the kinetic friction force. If that is larger than the static friction between A and B, then A will slip backwards. Static friction is not, in general the same as kinetic friction so just knowing that the force is greater than the sum of the two static frictions is not enough. It is true that, for most materials, the kinetic friction is less than the static friction. In that case, if force> static friction + static friction> kinetic friction + static friction, yes, A will move.

 

[baba89]

In this theoretical situation, if a force is applied on body B that is greater than the static friction with the floor and with body A, but smaller than their sum, then both bodies will experience a net force in the direction of the applied force. This means that both bodies will start to move in the direction of the applied force, but at different rates.

Body B, being the body with the greater applied force, will accelerate faster and move further than body A. However, body A will also experience a force in the same direction and will start to move, but at a slower rate compared to body B. This is because the force applied on body A is smaller than the static friction between body A and the floor, meaning there is still some resistance to its motion.

In conclusion, both bodies will move in the direction of the applied force, with body B moving faster and further due to the larger force applied. However, the motion of both bodies will still experience some resistance due to the static friction with the floor and between the bodies, preventing them from moving at their maximum potential.