Conservation of Momentum of a uniform thin rod

In summary, the conversation discusses a problem involving a uniform thin rod, a bullet, and conservation of momentum. The main question is what is the magnitude of the bullet's velocity just before impact. The conversation includes attempts at solving the problem and seeking clarification. Ultimately, the correct solution is found using conservation of angular momentum.
  • #1
7C0A0A5
10
0
A uniform thin rod of length 0.40 m and mass 3.5 kg can rotate in a horizontal plane about a vertical axis through its center. The rod is at rest when a 3.0-g bullet traveling in the horizontal plane of the rod is fired into one end of the rod. As viewed from above, the direction of the bullet's velocity makes an angle of 60° with the rod (Fig. 12-44).If the bullet lodges in the rod and the angular velocity of the rod is 14 rad/s immediately after the collision, what is the magnitude of the bullet's velocity just before impact? [in m/s]

12_44.gif


This should be a relatively easy problem, but I'm missing a concept somewhere. Please help.

First I thought that I could set Total Momentum before and after the collision equal to each other.
L = M can you do that?

[tex]L = I * \omega[/tex]
[tex]M = m * V[/tex]
[tex]I = {m_{final} * l^2}/12[/tex]
when solving these I got 0.04671 for L
and 218 for V
but that is wrong
then I used trig to find how fast that would be at that angle and got 252
which is also wrong...can someone please tell me where I'm messing up?
 
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  • #2
Did you first break the bullet's velocity into component vectors parallel and pendicular to the rod?
 
  • #3
Well...it doesn't give me the velocity of the bullet and that is what I'm trying to find...so when I solved for the velocity I got 218 m/s. But that is the velocity perpendicular to the plane, right? so then I divided that number by the cos of 30 and got 252 which is also wrong.
 
  • #4
7C0A0A5 said:
First I thought that I could set Total Momentum before and after the collision equal to each other.
L = M can you do that?
No. What you want to do is apply conservation of angular momentum.

You may find this discussion helpful: https://www.physicsforums.com/showthread.php?t=52632
 
  • #5
K thanks That thread did help and I got the right answer...don't fully understand why but I'll ask my proffesor during his office hours. Thanks a bunch guys.
 

1. What is the conservation of momentum of a uniform thin rod?

The conservation of momentum of a uniform thin rod is a fundamental principle in physics which states that the total momentum of a system remains constant unless acted upon by an external force. In the case of a uniform thin rod, the momentum is conserved due to the rod's constant mass and velocity.

2. How is the conservation of momentum applied to a uniform thin rod?

The conservation of momentum can be applied to a uniform thin rod by considering the rod as a system and analyzing the forces acting upon it. The momentum of the rod can be calculated using the formula p=mv, where p is the momentum, m is the mass, and v is the velocity. By analyzing the external forces acting on the rod and using the conservation of momentum principle, one can determine the final velocity of the rod after a collision or other event.

3. What is the importance of the conservation of momentum in understanding the behavior of a uniform thin rod?

The conservation of momentum is crucial in understanding the behavior of a uniform thin rod as it allows us to predict the motion of the rod in various situations. This principle is used in many areas of physics, including mechanics, thermodynamics, and electromagnetism. It also helps us understand the relationship between force, acceleration, and mass.

4. How does the length of a uniform thin rod affect its conservation of momentum?

The length of a uniform thin rod does not have a direct effect on its conservation of momentum. As long as the mass and velocity of the rod remain constant, the conservation of momentum will still apply. However, the length of the rod may affect its rotational motion, which can impact the conservation of angular momentum.

5. Can the conservation of momentum be violated in the case of a uniform thin rod?

No, the conservation of momentum cannot be violated in the case of a uniform thin rod. This principle is a fundamental law of physics and has been observed to hold true in all physical systems. In the case of a uniform thin rod, the conservation of momentum will always apply as long as there are no external forces acting on the rod.

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