A conceptual question regarding collision/conservation of energy.

[lillybeans]

Say there's the following situation:

A bullet with some velocity strikes a block connected to a spring. The bullet passes right through the block and the spring is compressed by x cm to the right of the block after the impact. Some internal energy is lost due to deformation of the block while bullet passes through it.

Because the question states "compressed AFTER the impact", i was able to assume that the only energy being converted into spring energy is the kinetic energy of the block (When it begins to compress when the bullet has already exited the block), so I solved the problem.

HOWEVER, WHAT IF the question had stated "the block compresses the spring DURING the impact", in other words, it compresses WHILE the bullet is passing through the block? Then would the spring energy come from BOTH the kinetic energy of the block and some of the kinetic energy of the bullet while it is moving through the block?

 

[ehild]

Good question. But the usual assumption when treating collision problems is that the collision happens instantaneously, that is so fast, that only the velocities change during the impact, nothing else. Of course, this is not true, the bullet needs some time to traverse the block, pushing material aside along its path, initialising reversible and irreversible effects on the block and on itself: exciting elastic waves, producing heat, sound, melting some material...
Ignoring the spring during collision, and treating compression of the spring by the block when the bullet left - it is a correct approximation.
The problem can not be solved otherwise, you would need to calculate the motion both the bullet and block during the impact, and for that you would need details of the interaction between bullet and block.

ehild

 

[lillybeans]

Good question. But the usual assumption when treating collision problems is that the collision happens instantaneously, that is so fast, that only the velocities change during the impact, nothing else. Of course, this is not true, the bullet needs some time to traverse the block, pushing material aside along its path, initialising reversible and irreversible effects on the block and on itself: exciting elastic waves, producing heat, sound, melting some material...
Ignoring the spring during collision, and treating compression of the spring by the block when the bullet left - it is a correct approximation.
The problem can not be solved otherwise, you would need to calculate the motion both the bullet and block during the impact, and for that you would need details of the interaction between bullet and block.

ehild

Thank you so much! That was an excellent explanation. May I ask further that if the situation had been "bullet strikes block and bounces back (elastic)", then is it also valid for me to assume that the block starts to move AFTER the bullet starts to bounce back? So I would ignore the spring's compression at the instant where the block-bullet moves together during the collision?

Lilly

 

[ehild]

May I ask further that if the situation had been "bullet strikes block and bounces back (elastic)", then is it also valid for me to assume that the block starts to move AFTER the bullet starts to bounce back? So I would ignore the spring's compression at the instant where the block-bullet moves together during the collision?

Lilly

Exactly. Ignore that short time when they move together, as you do not know how long it is.
There are some problems, when the time of interaction is given or can be computed - but you would notice if that is the case.

ehild

 

[asteriatic]

In this scenario, the conservation of energy principle still applies. The total energy before and after the collision must remain the same. However, the distribution of energy may be different.

If the block compresses the spring during the impact, then some of the kinetic energy of the bullet will indeed be converted into spring energy. This is because the bullet is still in contact with the block and is transferring some of its energy to it.

In this case, the total spring energy would come from both the kinetic energy of the block and the bullet. The amount of energy transferred from the bullet to the spring would depend on factors such as the mass and velocity of the bullet, the properties of the block and spring, and the duration of the impact.

It is important to note that the internal energy lost due to deformation of the block would still be a factor in this scenario. The amount of energy lost would also depend on the properties of the materials involved and the extent of deformation.

Overall, the key principle to keep in mind is that energy is always conserved in a closed system. The distribution and transformation of energy may vary depending on the specific circumstances of the collision.