Would it be easier to break a stack of planks joined together or when they have gaps between them? If there is a stack of n identical planks (say n=5) and we need to break them (like in karate), would it be easier (i.e. would it require less force) if they are stacked together (figure on the left) or if they have some gaps in between (figure on the right)?

 A: I think it would be easier if they were stacked together as in your first case, in contact with each other.
If the boards are layered with a gap in between each one,  then each board would have to bend then break before the next board is reached. This means your hand must touch and break each board one after the other.
When you stack many of them on top of each other in direct contact, the whole stack will bend together upon the one impact, and almost simultaneously fracture. If you ever watch a video of this by a martial artist, you will notice that his/her hand does not need to come in contact with nearly all the boards beneath the top one.
Also recall that the expression for force (from Newton’s second law)
$$F = \frac{m\Delta v}{\Delta t}$$
meaning a small value for the impact time $\Delta t$ will result in a larger value for the force $F$. The case where the boards are in contact, corresponds to a smaller value for $t$ as explained above. If the boards are layered with a gap in between each one,  then each board would have to bend then break before the next board is reached.
The first case (your right diagram) would require significantly more force than the second case (left diagram). So it would be easier for the case where they are placed in contact on top of each other.
A: what are impulsive forces

This can be understood by another reference

*

*when a stone is thrown over a window pane there is a huge crack since the stone had a Collison for larger time its impact was distributed overall and crack was observed for over a large area


*when a bullet strikes a window pane its contact with window pane lasts for a very short time and its impact is seen over a small area in the form of a neat hole
In short we say that the force in 2nd case is impulsive same is the case with breaking of planks
in case of plank
When you apply a force at ,maximum I.e perpendicular to the surface of planks you impart something called the impulsive force.
Suppose you apply N newton force on both sides
This forces act for a shot duration of time so i believe the time of action should be small therefore in figure a where there is no gap between planks the planks would break easily
A similar qo.
Impulse and force in a karate chop, can we maximize force minimizing the time of impact?
