Why does it keep getting harder to break a pencil in 2?

[mohamadh95]

Consider a pencil. Now break it in 2. Do it again and it s obvious it gets harder to do it. Why is that?
I thought of modeling the problems as a hinged beam with moments applied at both ends having opposite directions and same torque. So basically the length of the beam doesn't affect the moment diagram which constant and equal to the moments. As the beam length change we will still have the same moment distribution so why does it get harder? And what's the reason it breaks near the middle? Thank you.

 

[Merlin3189]

It's not clear to me just how you are holding this pencil. Perhaps you could post a diagram?

 

[mfb]

Usually you have a limited force you can apply. What happens to the moments if force stays the same but the length of the pencil fragement gets reduced?

 

[Aleena786]

your distance is decreasing from pivoted point, thus the total f*distance.. this should be greater then the limit.

 

[Rerry]

I agree, less torque with reduced surface area means less tension being applied to the pencil ! If you place said pencil in a fixed place, such as two eye hole screws. Put the pencil into these holes, which are spaced about a inch apart and you use your fingers to break the pencil. The applied pressure doesn't change, it's only when you hold the pencil in your hand that we notice the force needed doubles which each snap of the pencil. Basically it's to do with surface area and torque applied, less area means less torque unless it's in a fixed position as described above.