Collisions: Elastic vs inelastic

In summary, the bullet gains an initial velocity vinitial, and the target has an aerial friction that slows it down.
  • #1
lendav_rott
232
10
So there are a bunch of assignments in physics built on the conservation of momentum law where a bullet of some mass, hits a target of some mass, neglecting friction find the velocity at which the target starts moving. That is all very simple in case of an inelastic collision, all the energy of the bullet is transformed to the target+bullet mass, but what happens when it's a real scenario?

Assuming we know the mass of the bullet mb and the power behind the rifle - the bullet gains an initial velocity of vinitial. The target is, say, a metal sphere of mass ms at a distance of 200m - How do we calculate the aerial friction that slows down the bullet, assuming there is no wind to considerably change its direction?

At last the bullet hits the target at a velocity of vfinal. How much energy does the sphere exactly gain?
The bullet hits the sphere and bounces back,there is likely a dent in the sphere and the bullet is deformed, therefore some of the kinetic energy is transformed into mechanical energy and heat. Since the bullet bounces back I would assume it has something to do with Hooke's law, where the surface of the sphere is acting like a spring. How much energy is consumed by deformation and the spring? Is there a way to know how much of the energy the sphere "gets to use"? To what extent can we use the conservation of momentum in this scenario? What are all the elements we have to consider?
 
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  • #2
The flight of the bullet is studied in external ballistics. What happens when the bullet hits the target is studied in terminal ballistics. Things get hairy fairly quickly as soon as you start looking at the details.
 
  • #3
lendav_rott said:
So there are a bunch of assignments in physics built on the conservation of momentum law where a bullet of some mass, hits a target of some mass, neglecting friction find the velocity at which the target starts moving. That is all very simple in case of an inelastic collision, all the energy of the bullet is transformed to the target+bullet mass, but what happens when it's a real scenario?

Assuming we know the mass of the bullet mb and the power behind the rifle - the bullet gains an initial velocity of vinitial. The target is, say, a metal sphere of mass ms at a distance of 200m - How do we calculate the aerial friction that slows down the bullet, assuming there is no wind to considerably change its direction?
Assuming bullet's spherical: http://en.wikipedia.org/wiki/Stokes'_law
At last the bullet hits the target at a velocity of vfinal. How much energy does the sphere exactly gain?
Depends on coefficient of restitution: http://en.wikipedia.org/wiki/Coefficient_of_restitution
The bullet hits the sphere and bounces back,there is likely a dent in the sphere and the bullet is deformed, therefore some of the kinetic energy is transformed into mechanical energy and heat. Since the bullet bounces back I would assume it has something to do with Hooke's law, where the surface of the sphere is acting like a spring. How much energy is consumed by deformation and the spring?
Hooke's law doesn't apply after you reach yield strength:
http://en.wikipedia.org/wiki/Stress–strain_curve
After which elastic deformation gives way to:
http://en.wikipedia.org/wiki/Plastic_deformation#Plastic_deformation
Is there a way to know how much of the energy the sphere "gets to use"?
:confused:
KE should be given by coefficient of restitution, if that's what you mean.
To what extent can we use the conservation of momentum in this scenario? What are all the elements we have to consider?
Momentum should be conserved regardless of the type of collision.
 
  • #5
Forgot about the laminar flow clause... thanks for the correction;
I seem to be ticking with the IQ of a tick today...
 

FAQ: Collisions: Elastic vs inelastic

What is the difference between elastic and inelastic collisions?

Elastic collisions are those in which the total kinetic energy of the system is conserved, while inelastic collisions are those in which some kinetic energy is lost to internal energy or other forms of energy.

How can you determine if a collision is elastic or inelastic?

The best way to determine if a collision is elastic or inelastic is to calculate the total kinetic energy of the system before and after the collision. If the kinetic energy remains the same, the collision is elastic, but if it decreases, the collision is inelastic.

Are there any real-life examples of elastic and inelastic collisions?

Yes, there are many real-life examples of both types of collisions. For instance, a billiard ball collision is considered elastic because the total kinetic energy of the system remains the same. On the other hand, a car crash is an example of an inelastic collision because some kinetic energy is lost to deformation and sound.

How do elastic and inelastic collisions affect the objects involved?

In elastic collisions, the objects involved will experience a change in velocity and direction, but their overall shape and size will remain the same. In inelastic collisions, the objects will also experience a change in velocity and direction, but they may also undergo deformations or stick together.

Can elastic collisions ever become inelastic?

Yes, under certain conditions, an elastic collision can become inelastic. This can happen if there is a transfer of energy to other forms, such as heat or sound, or if the colliding objects undergo deformations. In these cases, the total kinetic energy of the system is not conserved, making the collision inelastic.

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