The Conservation of Momentum in a Completely Inelastic Collision.

In summary, the textbook says momentum is not conserved, but in the work it uses the conservative equation.
  • #1
student34
639
21

Homework Statement



A bullet with mass mA and velocity vA makes a completely inelastic collision with a still pendulum of mass B. After the collision, the pendulum swings to a height of y from its equilibrium with the bullet in it. In terms of y, mB and mA, what is the initial velocity?

My textbook says that momentum is not conserved because of the external forces of tension and gravity acting on the system; this makes sense to me. But, in my book's work, it gets the answer by using Pinitial = Pfinal, where the initial is the bullet's mass multiplied by its velocity, and the final momentum is both masses multiplied by their velocity in the +x direction. How can they say that momentum is not conserved and then use the conservative equation?

Homework Equations


The Attempt at a Solution

 
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  • #2
student34 said:
My textbook says that momentum is not conserved because of the external forces of tension and gravity acting on the system; this makes sense to me.
In general, that's true.

But, in my book's work, it gets the answer by using Pinitial = Pfinal, where the initial is the bullet's mass multiplied by its velocity, and the final momentum is both masses multiplied by their velocity in the +x direction. How can they say that momentum is not conserved and then use the conservative equation?
During the collision one usually assumes that the forces of impact are so great, and act for so short a time, that other forces can be neglected. This is called the impulse approximation.
 
  • #3
I think that the point being made is that DURING THE COLLISION (as Doc Al says) momentum is conserved.
After the collision you cannot use conservation of momentum to find the heigh 'y'.
You should use conservation of energy to find 'y' (KE = PE)
 
  • #4
Oh I see.

Thanks for the replies
 
  • #5


First of all, it is important to understand the concept of momentum and how it is conserved in a completely inelastic collision. Momentum is a property of an object that describes its motion and is the product of its mass and velocity. In a completely inelastic collision, the two objects stick together and move with a common final velocity after the collision.

In this scenario, the bullet and the pendulum stick together after the collision, forming a new system. The external forces of tension and gravity acting on the system do not affect the conservation of momentum within the system. This is because these forces act only within the system and do not involve any external objects.

Therefore, the conservation of momentum still holds true in this case, and the initial momentum of the system must be equal to the final momentum. This is why the equation Pinitial = Pfinal is used to solve for the initial velocity. It is important to note that this equation is a conservative equation and does not take into account any external forces.

In conclusion, the conservation of momentum is still applicable in a completely inelastic collision, even though there may be external forces acting on the system. These forces do not affect the momentum of the system, and therefore, the conservative equation can be used to solve for the initial velocity.
 

1. What is the conservation of momentum in a completely inelastic collision?

The conservation of momentum in a completely inelastic collision is a fundamental law of physics that states that the total momentum of a system of objects is conserved before and after the collision. This means that the total momentum remains the same, even if there is a transfer of momentum between the objects involved in the collision.

2. How is momentum conserved in a completely inelastic collision?

In a completely inelastic collision, the objects involved stick together after the collision and move as one combined object. Momentum is conserved in this type of collision because the total mass and velocity of the combined object remains the same as the sum of the masses and velocities of the individual objects before the collision.

3. What is the difference between a completely inelastic collision and an elastic collision?

In a completely inelastic collision, the objects involved stick together after the collision and move with a common velocity. In an elastic collision, the objects bounce off each other and have different velocities after the collision. Additionally, in an elastic collision, kinetic energy is conserved, while in a completely inelastic collision, some kinetic energy is lost and converted into other forms of energy, such as heat or sound.

4. Can the conservation of momentum be violated in a completely inelastic collision?

No, the conservation of momentum is a fundamental law of physics and cannot be violated. In a completely inelastic collision, the total momentum of the system is always conserved, regardless of any changes in the individual object's velocities or masses.

5. Why is the conservation of momentum important in the study of collisions?

The conservation of momentum is important in the study of collisions because it helps us understand and predict the outcome of collisions between objects. This law allows us to determine the velocities of objects after a collision and can be applied to many real-world scenarios, such as car crashes, sports collisions, and even celestial collisions.

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