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[SOLVED] Inelastic collision on a frictional surface
Sorry I clcked the wrong button and sent it out before typing anything... I didn't even catch up on the 30-min editting time. Please forgive my slow typing...
Homework Statement
A wood block with mass M was laid on a frictional surface with coefficient of kinetic friction u. A bullet with mass m flew towards the wook block with constant speed v; it shot into the block and moved along with the block for a distance before coming to rest. Given the force that the bullet experienced in the block was f, try to find out the distance D the block moved on the surface, and the distance d the bullet moved in the block.
Homework Equations
Work = Force x Distance (constant parallel force)
inelastic collision: m1 x v0 = (m1 + m2) x v
The Attempt at a Solution
I assumed that the collision was fast enough that the block didn't move apprecialbly during the collision, thus:
mv = (M+m)v'.............so v'=mv/(M+m)
and, with energetic considerations:
for bullet m: 1/2mv^2 - fd = 1/2mv'^2
for block M: 1/2Mv'^2 - u(M+m)gD = 0
I know my assumption may well be wrong, but I had no clue of doing it in another way. I didn't include any heat that was lost either, but I don't know how. I guess I don't understand the characteristics of frictional force very well. The wiki says the heat lost during a movement on a frictional surface is f x d... uh, why?
According to Newton's 3rd law, I thought that if the surface doesn't move, then the work that was "supposed to done by an object on the surface" is lost as heat.... but what if "the surface," as in the above case, IS moving? Also, if the earth served as "the surface", wouldn't it acquire a very very small acceleration when an object slides on it?
Why, then. does the enegy become heat but not the earth's kinetic energy?
According to Newton's 3rd law, I thought that if the surface doesn't move, then the work that was "supposed to done by an object on the surface" is lost as heat.... but what if "the surface," as in the above case, IS moving? Also, if the earth served as "the surface", wouldn't it acquire a very very small acceleration when an object slides on it?
Why, then. does the enegy become heat but not the earth's kinetic energy?
Conservation of energy was discovered nearly two centuries after Newton's lifetime, the long delay occurring because of the difficulty in understanding the role of microscopic and invisible forms of energy such as heat and infra-red light.
Since f was a lot larger than u(M+m)g and the stage lasted a very short time, this stage can be treated as an inelastic collision with no external force applying on the system. (I doubt the validity of this assumption)
Is that reasonable?
No, that's fine … momentum is ALWAYS conserved in collisions (whether elastic or not).
Well what I meant was, can that stage be seen as a collision? More specifically, can I split the process into stages? After all there was indeed a frictional force applied by the surface; that was an external force for my system. Besides, the original question did not state that f was large.![]()