Conservation of momentum and energy problem

In summary, the total angular momentum and total gravitational potential energy are the only quantities conserved in this process. The total mechanical energy, total linear momentum, and total kinetic energy are not conserved due to the introduction of the piece of clay, which can change the overall energy levels in the system.
  • #1
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Homework Statement


A uniform rod has a mass 2m and a length l, and it can spin freely in a horizontal plane about a pivot point O at the center of the rod. A piece of clay with mass m and velocity v hits
one end of the rod, and causes the rod-clay system to spin.
physics2.png


After the collisions the rod and clay system
has an angular velocity omega about the pivot.

Which quantity/quantities:

I) total mechanical energy
II) total linear momentum
III) total angular momentum with respect to pivot point O
IV) total gravitational potential energy
V) total kinetic energy

is/are conserved in this process?

Possible solutions:

1. III and IV only
2. II and III only - tried, was wrong
3. II, III, IV and V only
4. II, III and IV only
5. II and V only
6. I, II and III only
7. I only
8. None of these
9. III, IV and V only
10. All of these

The Attempt at a Solution



I tried II and III only as a solution, but it was wrong. I'm thinking that mechanical energy, kinetic energy, and gravitational potential energy are not conserved due to the introduction of a piece of clay, but it seems I'm wrong in some area. Can anyone help point me in the right direction?
 
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  • #2
Energy is always conserved.

If at any point in the system energy isn't conserved, it is either destroyed or created - is there something in the system that can do that? - is that even possible?

Linear momentum is always conserved.
 
  • #3
Total gravitational potential energy is not conserved (because the piece of clay that was at top originally ends up at the bottom). So any answer with IV in it is wrong, I'm thinking.

EDIT: woops, I thought it was vertical, not horizontal. OK, GPE should remain constant then.

EDIT2: Also, isn't kinetic energy lost in inelastic collisions? Total energy is always conserved, but kinetic energy may be converted into other forms of energy.
 
Last edited:
  • #4
EDIT: I'm referring to overall energy levels. I haven't seen anything in the question about inelastic.

Regardless, the overall energy level is conserved, but I suppose if you look at individual forms:

Kinetic increases - from clay to rod is constant.

GPE is constant - assuming we would ignore the fact the clay would technically add mass to the system. If not, it increases.
 
Last edited:
  • #5
The answer was #1, III and IV only.
 

1. What is conservation of momentum and energy?

Conservation of momentum and energy is a fundamental principle in physics that states that the total momentum and energy in a closed system remains constant over time. This means that in any interaction or process, the total amount of momentum and energy before and after the interaction remains the same.

2. Why is conservation of momentum and energy important?

Conservation of momentum and energy is important because it allows us to predict and understand the behavior of objects and systems in motion. It also helps us to analyze and solve problems related to collisions, explosions, and other interactions between objects.

3. How is conservation of momentum and energy related?

Conservation of momentum and energy are related in that they both involve the idea of a closed system. In a closed system, the total amount of momentum and energy remains constant, meaning that any changes in momentum must be balanced by changes in energy, and vice versa.

4. What are some real-life examples of conservation of momentum and energy?

One example of conservation of momentum and energy is a pool game. When a cue ball strikes a stationary ball, the total momentum and energy of the two balls before and after the collision remains the same. Another example is a roller coaster, where the potential energy at the top of the first hill is converted into kinetic energy as the coaster moves down the track.

5. Can conservation of momentum and energy be violated?

No, conservation of momentum and energy is a fundamental law of physics and cannot be violated in a closed system. However, in open systems where external forces are present, the total momentum and energy may change due to the work done by these forces. This is known as the principle of conservation of momentum and energy.

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