Energy Loss in Head on Collision of Two Cars w/Same Speed and Mass

In summary, when two cars collide head-on, some of their kinetic energy is lost in the form of heat, sound, and deformation of the cars, a phenomenon known as collision energy loss. The amount of energy lost depends on factors such as the speed and mass of the cars, the materials and design of the cars, and the angle and force of impact. However, not all the energy is lost, as some is used to deform the cars and is converted into other forms. The mass of the cars also plays a significant role, with heavier cars experiencing less energy loss due to their ability to resist change in motion. While energy loss in a head-on collision cannot be completely prevented, safety features and safe driving practices can help reduce it.
  • #1
mrsteve
9
0

Homework Statement



Two railroad cars, each with a mass of 7,000kg and traveling at 90 km/h collide head on and come to rest. How much mechanical energy is lost in this collision?

Homework Equations



[tex]KE=\frac{1}{2}mv^2[/tex]

The Attempt at a Solution



[tex]KE=\frac{1}{2}(7000)(90)^2=2.835*10^7[/tex]

Mechanical energy = KE+PE. PE = 0.

Energy lost = 2KE or [tex]5.67*10^7[/tex]

Book answer is [tex]4*10^6[/tex]

Where am I going wrong? Thanks..
 
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  • #2
If your result is in joules, the velocity units of km/h is not helping.
 
  • #3
Convert the speed to standard units of m/s.
 
  • #4
Ahh... So 90 km/h = 25 m/s.

[tex]\frac{1}{2}(7000)(25)^2=2.1875*10^6 => 2.1875*10^6(2) = 4.375*10^6 => 4*10^6[/tex]

Thanks!
 
  • #5




In this scenario, the total mechanical energy before the collision is equal to the sum of the kinetic energies of the two cars. However, after the collision, the cars come to a complete stop, meaning that the final kinetic energy is equal to zero. This means that the total mechanical energy after the collision is also equal to zero, as there is no potential energy involved. Therefore, the energy lost in this collision is equal to the initial mechanical energy, which is 2.835*10^7 Joules.

The book answer of 4*10^6 Joules may be referring to the energy lost by each individual car, rather than the total energy lost in the collision. In this case, the energy lost by each car would be half of the initial mechanical energy, which is 1.4175*10^7 Joules. It is important to clarify the context and assumptions made in a problem in order to arrive at the correct answer.
 

Related to Energy Loss in Head on Collision of Two Cars w/Same Speed and Mass

1. How is energy lost in a head-on collision of two cars with the same speed and mass?

In a head-on collision, the cars involved experience an abrupt change in velocity. This change in velocity results in a transfer of kinetic energy, causing some of the energy to be lost in the form of heat, sound, and deformation of the cars. This energy loss is known as collision energy loss.

2. What factors affect the amount of energy lost in a head-on collision?

The amount of energy lost in a head-on collision depends on several factors, including the speed and mass of the cars, the materials and design of the cars, and the angle and force of impact. In general, higher speeds and masses result in greater energy loss.

3. Is all the energy lost in a head-on collision?

No, not all the energy is lost in a head-on collision. Some of the energy is used to deform the cars and overcome the internal forces that resist the change in motion. Additionally, some of the kinetic energy is converted into other forms, such as heat and sound. However, the total amount of energy remains the same before and after the collision, according to the law of conservation of energy.

4. How does the mass of the cars affect the energy loss in a head-on collision?

The mass of the cars plays a significant role in the amount of energy lost in a head-on collision. In a collision between two cars with the same speed but different masses, the heavier car will experience less change in velocity and therefore less energy loss. This is because the greater mass of the car allows it to better resist the change in motion.

5. Can energy loss in a head-on collision be prevented?

Energy loss in a head-on collision cannot be completely prevented, but it can be reduced by implementing safety features such as crumple zones, airbags, and seat belts. These features are designed to absorb and distribute the energy of the collision, reducing the impact on the occupants and minimizing the overall energy loss. Additionally, following traffic laws and maintaining a safe driving speed can also help prevent head-on collisions and reduce energy loss.

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