Trying to find out how to calculate how fast something moves from the force In our introductory physics class (8th grade) I/we would like to find out how fast a piece of paper needs to be moving to break a chopstick. [Similar to putting a straw through a potato]
We will be finding the average Newtons via an apparatus using leverage and finding what N makes the chopstick break. From THAT, I am curious about how to derive the speed the paper needs to move at the break. {For MY curiosity and the advanced and inquisitive students}
We use a wire loop to afford the same area through which the paper travels, so pressure should be equal. Been a few years since I did this last and notes/computer handouts are MIA since upgrades and changing schools. We came up with the paper of about three grams yielding 1000 m/s.
We know that the paper was not supersonic, not making the whip-crack as we break the chopstick, so wondering where I calculated incorrectly.
 A: There is no particular answer to this problem.
The force which will act on the chopstick upon collision is dependent on how quickly the paper comes to rest upon collision by decelerating (specifically, it's rate of change of momentum will determine the force exerted). If we assume the chopstick to be brittle in nature (assuming it is built in a way which makes it incapable of exhibiting plastic behavior), the chopstick will get fractured if the force is large enough to take it out of the elastic region. The problem is that you cannot determine the deceleration of the paper theoretically, as the hardness/softness of the chopstick will directly determine this. There is no way (at least no way I know of) around this problem without actually performing a series of experiments and timing how long the collision last for. The average force exerted will be $F= m \frac{\delta v}{\delta t}$. It's not initial velocity of the paper that matters, but rather it's mass and how quickly it's brought to rest.
