Car-Car System: Energy Conservation?

In summary, the conversation discusses the solution for a car-car system, which involves the law of conservation of energy and considers the velocities and masses of the cars. The thermal energy produced is found to be dependent on the frame of reference, but the kinetic energy post-collision is consistent in all frames. The conversation concludes that there is no need to ask further questions as the solution will be encountered again in the future.
  • #1
simphys
324
46
Homework Statement
(I) Two railroad cars, each of mass 56,000 kg, are traveling
##95km/h##toward each other. They collide head-on and come
to rest. How much thermal energy is produced in this collision?
Relevant Equations
law of conserfvation of energy
this is an easy problem but would it be possible to consider car-car system. What I did on paper was carsystem and because they have the same properties(mass en speed) multiply by ##2##

solution for car-car-earth system I assume is the following if it is possible?

solution for car-car:
law or conservation of energy says:

##E_1 = E_2 + W_{th}##
##\frac12m_{c1}v_{1,c1}^2 + \frac12m_{c2}v_{2,c2}^2 = 0 + W_{th}##
massses same, velocity same so :
##W_{th} = mv^2 = 3.9E7J##

edit: What I actually want reassurance of is.. this is all dependent on the system and if we take car-car system we consider all the energies of the involved objects by examining all of 'em seperately. I am asking stuff like this because it's kinda important but not really mentioned only implicitly in the book
Thanks in advance

Edit: ;earth not included
 
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  • #2
It is not dependent on the frame. If the cars have velocities ##\pm v## in the cener of mass frame then the thermal energy produced is indeed ##mv^2## as you have concluded. If you instead consider a frame moving with velocity ##u## relative to the center of mass system then the velocities of the cars are ##\pm v - u## and consequently the energy before collision
$$
W_0 = \frac{m}{2}[(v-u)^2 +(v+u)^2] = m(v^2 + u^2).
$$
After collision the cars are moving at velocity ##u## and so the kinetic energy post-collision is
$$
W_k = \frac{2m}{2} u^2 = m u^2.
$$
The thermal energy produced is therefore ##W_0-W_k = mv^2##, just as found in the center of mass frame.
 
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  • #3
Orodruin said:
It is not dependent on the frame. If the cars have velocities ##\pm v## in the cener of mass frame then the thermal energy produced is indeed ##mv^2## as you have concluded. If you instead consider a frame moving with velocity ##u## relative to the center of mass system then the velocities of the cars are ##\pm v - u## and consequently the energy before collision
$$
W_0 = \frac{m}{2}[(v-u)^2 +(v+u)^2] = m(v^2 + u^2).
$$
After collision the cars are moving at velocity ##u## and so the kinetic energy post-collision is
$$
W_k = \frac{2m}{2} u^2 = m u^2.
$$
The thermal energy produced is therefore ##W_0-W_k = mv^2##, just as found in the center of mass frame.
wow that's aamazinggg thanks a lot! I guess I don't need to ask such question then as I'll most likely encounter that soon myself
 

Related to Car-Car System: Energy Conservation?

1. What is a Car-Car System?

A Car-Car System is a type of energy conservation technology that utilizes two or more cars to work together and conserve energy. It involves creating a physical connection between the vehicles, usually through a specialized device, to allow them to move in tandem and use less energy.

2. How does a Car-Car System conserve energy?

A Car-Car System conserves energy by allowing multiple cars to work together, reducing the amount of energy needed to move each individual vehicle. By creating a physical connection between the cars, the system can distribute the energy needed for movement more efficiently, resulting in overall energy conservation.

3. What are the benefits of using a Car-Car System?

There are several benefits to using a Car-Car System. First, it can significantly reduce fuel consumption and emissions, making it an environmentally friendly option. It can also increase the efficiency of transportation and reduce traffic congestion. Additionally, it can save drivers money on fuel costs.

4. Are there any drawbacks to using a Car-Car System?

While there are many potential benefits to using a Car-Car System, there are also some drawbacks to consider. One potential issue is the need for specialized equipment and technology, which can be costly and may require additional maintenance. There may also be challenges in coordinating and synchronizing the movement of multiple vehicles, especially in busy traffic situations.

5. How widely used is the Car-Car System currently?

The Car-Car System is still a relatively new technology and is not widely used at this time. However, there is ongoing research and development in this area, and some companies and organizations are beginning to implement and test the system. As more studies and trials are conducted, we may see an increase in the use of Car-Car Systems in the future.

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