Elastic vs. Inelastic Collisions: Which is Better for Diverting an Asteroid?

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In summary, the conversation discusses the best approach for diverting an asteroid heading towards Earth as a scientist or engineer working for NASA. The question is whether it is better to make an elastic or inelastic collision with the asteroid in order to change its momentum by the greatest amount. There is a debate between the two options, with the possibility of an inelastic collision being the best but potentially impossible. The question also raises concerns about the projectile potentially heading towards Earth after an elastic collision. Finally, there is a discussion about force required to stop the projectile in both types of collisions.
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Homework Statement



Let’s say you’re a scientist or engineer working for NASA and you are tasked with the responsibility of diverting an asteroid heading straight for Earth. You know that you must fire a projectile to deflect the asteroid as much as possible (without breaking it into many Earth-destroying pieces!). In the hopes of changing the asteroid’s momentum by the greatest amount, would you want your projectile to make an elastic or inelastic collision with the asteroid? Briefly explain.

Homework Equations





The Attempt at a Solution



I thought that making an inelastic collision would be the best, but probably impossible. Also if we make an elastic collision, wouldn't the projectile head towards Earth after it collides with the asteroid?

I want to hear your opinions on this.
 
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  • #2
Which requires more force.

1. Stop the projectile with a velocity of v (inelastic collision).

2. Stop the projectile with a velocity of v and then speed up the same projectile with a velocity of v in the opposite direction (elastic collision).
 

FAQ: Elastic vs. Inelastic Collisions: Which is Better for Diverting an Asteroid?

1. What is an elastic collision?

An elastic collision is a type of collision where the total kinetic energy of the system is conserved. This means that the total energy before the collision is equal to the total energy after the collision. In other words, the kinetic energy is transferred between the two objects involved in the collision without any energy being lost or gained.

2. What is an inelastic collision?

An inelastic collision is a type of collision where the total kinetic energy of the system is not conserved. This means that some of the kinetic energy is lost in the form of heat, sound, or deformation of the objects involved in the collision. In an inelastic collision, the total energy after the collision is less than the total energy before the collision.

3. How can the coefficient of restitution be used to determine the type of collision?

The coefficient of restitution is a measure of the elasticity of a collision. It is defined as the ratio of the relative velocity of separation to the relative velocity of approach between two objects after a collision. A coefficient of restitution equal to 1 indicates an elastic collision, while a coefficient less than 1 indicates an inelastic collision.

4. What is the conservation of momentum in collisions?

The conservation of momentum states that the total momentum of a closed system remains constant in both elastic and inelastic collisions. This means that the total momentum of the objects involved in the collision before the collision is equal to the total momentum after the collision. This principle is based on Newton's third law of motion.

5. How do you calculate the final velocities of objects in an elastic collision?

In an elastic collision, the final velocities of the objects involved can be calculated using the conservation of momentum and conservation of kinetic energy equations. These equations take into account the masses and velocities of the objects before and after the collision. The final velocities can also be determined experimentally by measuring the velocities of the objects before and after the collision.

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