A conceptual question regarding collision/conservation of energy.

In summary, when dealing with collision problems, the usual assumption is that the collision happens instantaneously and only the velocities change during the impact. However, this is not entirely accurate as the bullet needs some time to traverse the block, resulting in reversible and irreversible effects such as elastic waves, heat, sound, and material deformation. If the question states that the block compresses the spring during the impact, then the spring energy would come from both the kinetic energy of the block and some of the kinetic energy of the bullet. However, if the question states that the block compresses the spring after the impact, then it is valid to assume that the block only starts to move after the bullet starts to bounce back, and the spring's compression during the
  • #1
lillybeans
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1
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?
 
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Likes Neha Siddhartha
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  • #2
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
 
  • #3
ehild said:
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
 
  • #4
lillybeans said:
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
 
  • #5


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.
 

1. What is the concept of conservation of energy?

The concept of conservation of energy states that energy cannot be created or destroyed, but can only be transferred or converted from one form to another. This means that the total amount of energy in a closed system remains constant over time.

2. How does the conservation of energy apply to collisions?

In collisions, the total amount of kinetic energy before and after the collision remains the same. This is because the energy is transferred from one object to another, but the total amount remains constant. This is known as the law of conservation of momentum.

3. What factors affect the conservation of energy in collisions?

The conservation of energy in collisions is affected by factors such as the mass and velocity of the objects involved, the type of collision (elastic or inelastic), and external forces acting on the system.

4. Can energy be lost in a collision?

In an ideal system, where there are no external forces acting on the objects, the total amount of energy remains constant. However, in real-world situations, some energy may be lost due to factors such as friction and heat. This means that the total energy after the collision may be slightly less than the initial amount.

5. How is the conservation of energy related to the first law of thermodynamics?

The first law of thermodynamics states that energy cannot be created or destroyed, but can only be transferred or converted. This is essentially the same concept as the conservation of energy, as both state that the total amount of energy in a closed system remains constant.

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