Conservation of energy in a bullet-wooden block impact system

[PHYSICSSSTUDENT]

Suppose a bullet with high speed strike a wooden block and move together after collision. We know there is loss in total KE of bullet-wooden block system. The question is, if the part of the loss in KE of the bullet is transfer to heat energy, HOW to prove the CONSERVATION of ENERGY in this case, where FRICTIONAL WORK = LOSS in KE of the BULLET?

 

[ZapperZ]

Suppose a bullet with high speed strike a wooden block and move together after collision. We know there is loss in total KE of bullet-wooden block system. The question is, if the part of the loss in KE of the bullet is transfer to heat energy, HOW to prove the CONSERVATION of ENERGY in this case, where FRICTIONAL WORK = LOSS in KE of the BULLET?

Why do you need to prove this?

The stoppage of a bullet in a block is more complicated than that. It isn't JUST from the frictional force. There may also be energy loss via sound, etc. So it isn't just transferred to heat, i.e. it is not just ONE single channel of energy loss.

Unless you, or the problem, allows you to make simplifying ASSUMPTIONS, i.e. say that all energy loss is ONLY via thermal energy due to friction, you cannot "prove" that "frictional work = loss of KE of the bullet".

Zz.

 

[PHYSICSSSTUDENT]

Why do you need to prove this?

The stoppage of a bullet in a block is more complicated than that. It isn't JUST from the frictional force. There may also be energy loss via sound, etc. So it isn't just transferred to heat, i.e. it is not just ONE single channel of energy loss.

Unless you, or the problem, allows you to make simplifying ASSUMPTIONS, i.e. say that all energy loss is ONLY via thermal energy due to friction, you cannot "prove" that "frictional work = loss of KE of the bullet".

Zz.

Because I wonder how the principle of conservation of energy can apply to any problem, thanks for your reply from which I know there may also be energy loss via sound.

 

[sophiecentaur]

HOW to prove the CONSERVATION of ENERGY

The TOTAL energy in the system is conserved so you have to count every component during the collision. Something will get warm and distort permanently, perhaps and you will hear the impact.
Momentum will be conserved, though.

 

[PHYSICSSSTUDENT]

The TOTAL energy in the system is conserved so you have to count every component during the collision. Something will get warm and distort permanently, perhaps and you will hear the impact.
Momentum will be conserved, though.

I am interested in how energy is conserved in this process. I knew momentum will always be conserved but not the total KE. So, I don't know how to count every particle during the collision. You know, friction is a mysterious thing.

 

[anorlunda]

You know, friction is a mysterious thing.

Yes indeed. And friction is just an average representing a very complicated interface at the molecular level.

Proving conservation of energy in a setup like you describe is very difficult. There are so many forms of energy, and it can be so difficult to measure small quantities. But the important question is how accurate do you need to be to consider it proved?

 

[FactChecker]

The bullet will expend energy by forming a hole in the wood. The hole represents work done in multiple opposing directions, so it uses energy but produces much less single-direction kinetic energy. This is more obvious where the bullet is buried in something that can splatter in all directions, like a watermelon.

 

[sophiecentaur]

So, I don't know how to count every particle during the collision. You know, friction is a mysterious thing.

You can't, which is why we use a macroscopic approach. If you want an example of how particles can be related to macroscopic behaviour then look at the Kinetic Theory of Gases. No one is interested in what the individual gas molecules are doing but the statistics describe how a gas will behave very well.

Friction is only as 'mysterious' as all the rest of mechanics but the word is so often used and defined in a confusing way. If you stick with it as a Force that's parallel with two surfaces which opposes other parallel forces then you're OK. It's when it's described just as a force that 'slows things down' that the confusion arises.

 

[A.T.]

And friction is just an average representing a very complicated interface at the molecular level.

The same is true for the normal force or pressure.

 

[sophiecentaur]

The same is true for the normal force or pressure.

True but the normal force doesn't seem to present people with quite the same confusion. Perhaps because its direction is easier to identify.
'The normal force is a force that keeps things apart', is a bit more straightforward and it's mostly true, too.

 

[FactChecker]

Suppose a bullet with high speed strike a wooden block and move together after collision. We know there is loss in total KE of bullet-wooden block system. The question is, if the part of the loss in KE of the bullet is transfer to heat energy, HOW to prove the CONSERVATION of ENERGY in this case, where FRICTIONAL WORK = LOSS in KE of the BULLET?

It is impossible to prove this in any arbitrary experiment starting from scratch. That is the difference between a well-designed experiment and a poorly designed experiment. There are well-designed experiments where the increase in temperature due to friction would prove the conservation principle. That can not be proven in every conceivable situation, it must be assumed based on the good experiments.

 

[Mister T]

The question is, if the part of the loss in KE of the bullet is transfer to heat energy, HOW to prove the CONSERVATION of ENERGY in this case, where FRICTIONAL WORK = LOSS in KE of the BULLET?

The internal energy of both the bullet and the wooden block will increase. I'm not sure what you mean by "prove". If you take simpler examples you can account for the increase in internal energy by measuring the temperatures of the objects before and after the collision. Changes in temperature are related to the amount of energy transferred. Do a google search for mechanical equivalent of heat.

 

[Leontas]

A gross simplification I think is to theoryticaly accept a time duration of the collision. Then take into account the third law, the deceleration of the bullet and the acceleration of the target until they have common speed. If you accept only friction like forces you can calculate the work done by these forces. I think such calculations are in most textbook's excersises.
If you do not accept only friction like forces I think it is impossible to prove anything as the others already told you.

 

[sophiecentaur]

How would you define a “friction like” force and distinguish it from hysteresis losses?

 

[Leontas]

How would you define a “friction like” force and distinguish it from hysteresis losses?

A) F=T=constant
B) hysterisis due to deformation? Not distinguishable as long as Fdeformation=constant
As per op he talked about heat so the gross simplification is to accept only friction like forces. If he chooses to be fine with constant deformation force (at the same direction of the movement) then so be it.