Clay-stick inertia & energy problem

In summary: Mechanical energy is still conserved because the total momentum of the system is still the same.In summary, the collision between the stick and the clay creates a system with an increase in mass and a decrease in velocity. The final mechanical energy is greater than the initial mechanical energy.
  • #1
MickeyBlue
26
2

Homework Statement


A thin stick of mass M = 2.8 kg and length L = 2.2 m is hinged at the top. A piece of clay, mass m = 0.8 kg and velocity V = 2.7 m/s hits the stick a distance x = 1.65 m from the hinge and sticks to it.

Q2: What is the ratio of the final mechanical energy to the initial mechanical energy?

Homework Equations


1. Lf = Li (conservation of angular momentum)
2. Is = ⅓ML2
3. Ic = mx2
4. Krot = ½Iω2
5. Kl =½mVt2

The Attempt at a Solution


Clay-stick problem.jpg

I can't find the problem with my working in part 2; wondering if someone can point me in the right direction please. I calculated the angular velocity as 0.53 rad/s.
 
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  • #2
MickeyBlue said:

Homework Statement


A thin stick of mass M = 2.8 kg and length L = 2.2 m is hinged at the top. A piece of clay, mass m = 0.8 kg and velocity V = 2.7 m/s hits the stick a distance x = 1.65 m from the hinge and sticks to it.

Q2: What is the ratio of the final mechanical energy to the initial mechanical energy?

Homework Equations


1. Lf = Li (conservation of angular momentum)
2. Is = ⅓ML2
3. Ic = mx2
4. Krot = ½Iω2
5. Kl =½mVt2

The Attempt at a Solution


View attachment 106431
I can't find the problem with my working in part 2; wondering if someone can point me in the right direction please. I calculated the angular velocity as 0.53 rad/s.
I get almost the same, but you might have some rounding error. Keep another digit of precision all the way through. I get .325.
I note that it asks for the ratio, so technically the answer should be of the form 0.32:1. Do you know what the official answer is?
 
  • #3
No, I don't have an official answer yet. I thought the same about the ratio, but my online submission doesn't recognise colons.
 
  • #4
I'd like to follow up from my previous answer: if the clay and the stick are taken as one system, and we assume no friction about the pivot, is the case not that mechanical energy is conserved? That would make the ratio 1:1 (or just 1).

I'm not 100% sure on this.
 
  • #5
MickeyBlue said:
I'd like to follow up from my previous answer: if the clay and the stick are taken as one system, and we assume no friction about the pivot, is the case not that mechanical energy is conserved? That would make the ratio 1:1 (or just 1).

I'm not 100% sure on this.
The initial mechanical energy must be that before the collision. Since the bodies coalesce, it cannot be conserved.
 

1. What is the "clay-stick inertia & energy problem"?

The clay-stick inertia & energy problem is a scientific concept that refers to the difficulty in modeling the behavior of a system in which a stick is attached to a piece of clay. This system exhibits complex dynamics due to the combination of the stick's inertia and the energy stored in the clay.

2. How does the clay-stick inertia & energy problem relate to Newton's laws of motion?

The clay-stick inertia & energy problem is a manifestation of Newton's laws of motion. Specifically, it highlights the challenges in accurately predicting the motion of an object when both inertia and energy are involved. This problem is often used to illustrate the limitations of Newton's laws and the need for more advanced theories of motion.

3. Can the clay-stick inertia & energy problem be solved using classical mechanics?

No, the clay-stick inertia & energy problem cannot be solved using classical mechanics alone. This is because classical mechanics does not take into account the energy stored in the clay, which is a crucial factor in this problem. To accurately model this system, one must use more advanced theories, such as Lagrangian or Hamiltonian mechanics.

4. What are some real-world applications of the clay-stick inertia & energy problem?

The clay-stick inertia & energy problem has many practical applications, such as in robotics and biomechanics. Understanding the complex dynamics of this system can help in designing more efficient and stable robotic arms or in studying the movement of biological systems, such as the human arm.

5. Are there any proposed solutions to the clay-stick inertia & energy problem?

Yes, there have been various proposed solutions to the clay-stick inertia & energy problem, such as the use of non-linear theories of motion or incorporating the energy stored in the clay into the equations of motion. However, there is still ongoing research in this area to find a more comprehensive solution that can accurately model the behavior of this system.

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