Newton's laws of motion discussion question

[madah12]

this is from chapter 4 of university physics of young and freedman
q19 why can it hurt your foot more to kick a big rock than a small pebble? must the big rock hurt more? explain?
but I can't see the answer at all by just applying Newtons law
in the scenario of the small pebble
m_p is small
you apply a force F to the pebble it applies the same force on your foot and get a_p = F/m_p
and you get a_f=F/m_f

incase of the large rock
m_r>m_p

but the same F is applied the acceleration =F/m_r
and a_f=F/m_f
so the acceleration of your foot is independent of the mass of the kicked object as I see and the only difference is that the pebble will get more acceleration so how by Newtons laws can I answer this question? is it related to other concepts? if so why ask it in the Newton's laws section?

 

[Doc Al]

You are assuming that you apply the same force to both pebble and rock. But which is most likely to require generating larger amounts of force? Which is harder to accelerate?

 

[madah12]

well in the question you only kick the rock you don't have to move it the same distance but ok if you want me to assume that you want to accelerate the rock the same acceleration of the pebble then the it would always hurt more to hit the heavier rock so the second part doesn't make sense...
but my point is that it doesn't matter why what do you kick because the force you will feel is the force you will apply right? the kicked object's mass only affect the acceleration "it" not the acceleration I would received right?

 

[Doc Al]

well in the question you only kick the rock you don't have to move it the same distance but ok if you want me to assume that you want to accelerate the rock the same acceleration of the pebble then the it would always hurt more to hit the heavier rock so the second part doesn't make sense...

Imagine you have two identical-looking rocks in front of you. Unknown to you, only one is a real heavy rock, the other is just a light, plastic fake rock. You attempt to kick each one in a similar manner with a hard, swift kick. What happens?

As far as part 2 goes, it seems ambiguous. Does kicking a heavy rock have to hurt more? Of course not. Kick the rock very lightly; kick the pebble as hard as you can.

 

[madah12]

Imagine you have two identical-looking rocks in front of you. Unknown to you, only one is a real heavy rock, the other is just a light, plastic fake rock. You attempt to kick each one in a similar manner with a hard, swift kick. What happens?

As far as part 2 goes, it seems ambiguous. Does kicking a heavy rock have to hurt more? Of course not. Kick the rock very lightly; kick the pebble as hard as you can.

the light one will accelerate more while the heavy one will accelerate less
also how do we look at this from impulse momentum point of view? from experience when I kick a heavy rock my feet bounce back a little but if i hit a small one it goes forward so is the impulse at the first scenario bigger than the initial momentum but opposite in direction? while it isn't bigger in the second? does the fact the my feet bounce back have to do with the amount of pain my I feel?

 

[russ_watters]

the light one will accelerate more while the heavy one will accelerate less

And what does that say about the acceleration of your foot?