Question about vibrational kinetic energy and potential energy.

In summary, the conversation discussed the scenario of two blocks connected by a spring, with one block being held at rest and a larger upward force being suddenly applied. The heights of the centers of the blocks were given, and the increase in total translational kinetic energy of the blocks was calculated. The conversation then moved on to considering the real system and calculating the increase in vibrational kinetic energy and potential energy. The equations used were W=fd and K+U (total)= K(trans) + K(vib) + U. The solution for part "a" was 10.56 J. The solution for part "b" was 18.8 J, but the accuracy of this answer was uncertain.
  • #1
dizzid122
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Homework Statement


You hold up an object that consists of two blocks at rest, each of mass M = 3 kg, connected by a low-mass spring. Then you suddenly start applying a larger upward force, of constant magnitude F = 94 N (which is greater than 2Mg). Some time later, the blocks have moved upward, and the spring stretch has increased.

The heights of the centers of the two blocks are as follows:
Initial and final positions of block 1: y1i = 0.1 m, y1f = 0.2 m
Initial and final positions of block 2: y2i = 0.4 m, y2f = 0.9 m

It helps to show these heights on a diagram. Note that the initial center of mass of the two blocks is (y1i + y2i)/2, and the final center of mass of the two blocks is (y1f + y2f)/2.

(a) Consider the point particle system corresponding to the two blocks and the spring. Calculate the increase in the total translational kinetic energy of the two blocks. It is important to draw a diagram showing all of the forces that are acting, and through what distance each force acts.

(b) Consider the real system corresponding to the two blocks and the spring. Calculate the increase of (Kvib+Us), the vibrational kinetic energy of the two blocks (their kinetic energy relative to the center of mass) plus the potential energy of the spring. It is important to draw a diagram showing all of the forces that are acting, and through what distance each force acts.



Homework Equations


W=fd
K+U (total)= K(trans) + K(vib) + U, etc.
There may be other equations needed, I'm not sure...


The Attempt at a Solution


I got part "a" correct with an answer of 10.56 J. It's part "b" I'm having issue with. Here's what I'm currently thinking.

W=94*.5 (This would give me the total K+U, as block 2 is the part of the system the force is actually affected, it's being pulled up on? maybe?) = 47 J

47-10.56 (the translational kinetic energy)-(9.8*6*.3) (Potential energy of Earth with the system, mgh, with h being the change in height of the center of mass of the system).
=18.8 J. I am however, not very confident in this answer. Any help, especially with a method explaining what to do, would be greatly appreciated, thanks!
 
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  • #2
Unless I'm missing something this is a hard problem. It would probably help others if you included a scan of your work that got you the right answer to the first part, then others might better be able to help.

Interesting problem, not feeling very sharp right now.
 

1. What is vibrational kinetic energy and potential energy?

Vibrational kinetic energy is the energy associated with the motion of atoms or molecules within a substance. This energy is due to the vibrations of the atoms or molecules around their equilibrium positions. Vibrational potential energy, on the other hand, is the energy stored in the bonds between atoms or molecules, which is released during the vibrations.

2. How do vibrational kinetic energy and potential energy affect the properties of a substance?

The amount of vibrational kinetic energy and potential energy in a substance directly affects its physical properties such as temperature, density, and viscosity. For example, substances with higher amounts of vibrational energy tend to have higher temperatures and are more fluid due to the increased movement of the particles.

3. What factors affect the amount of vibrational kinetic energy and potential energy in a substance?

The amount of vibrational energy in a substance is affected by the temperature of the substance, the mass and type of particles, and the strength of the bonds between particles. Higher temperatures, lighter particles, and weaker bonds all result in higher amounts of vibrational energy.

4. How is vibrational kinetic energy and potential energy related to other forms of energy?

Vibrational energy is a type of mechanical energy, as it is associated with the movement of particles. It is also related to thermal energy, since an increase in vibrational energy results in an increase in temperature. Similarly, vibrational potential energy is a form of potential energy, which can be converted into kinetic energy during vibrations.

5. How is vibrational kinetic energy and potential energy measured or calculated?

Vibrational kinetic energy and potential energy can be calculated using the equations for kinetic and potential energy, respectively. The amount of vibrational energy can also be measured using techniques such as infrared spectroscopy, which measures the vibrational frequencies of molecules, or calorimetry, which measures the amount of heat released during vibrations.

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