Change in kinetic energy in a 2-car collision

In summary, the conversation discusses a solved problem involving the change in kinetic energy in a 2-car collision. The cars are equipped with flexible bumpers, causing less damage during low-speed collisions. The initial and final speeds of the cars are given, allowing for the calculation of the change in kinetic energy. It is clarified that only momentum is conserved in this collision, not kinetic energy.
  • #1
clope023
992
131
[SOLVED] change in kinetic energy in a 2-car collision

Homework Statement



When cars are equipped with flexible bumpers, they will bounce off each other during low-speed collisions, thus causing less damage. In one such accident, a 1850kg car traveling to the right at 1.60m/s collides with a 1450kg car going to the left at 1.10m/s . Measurements show that the heavier car's speed just after the collision was 0.270m/s in its original direction. You can ignore any road friction during the collision.

a) What was the speed of the lighter car just after the collision?

got this to be .597m/s

b) (where I'm stuck) Calculate the change in the combined kinetic energy of the two-car system during this collision.

Homework Equations



[tex]\Delta[/tex]K = K2-K1?


The Attempt at a Solution



I'm pretty sure I'm missing something obvious, but I'v tried like 5 different combinations.

(1/2(ma + mb)(v2a+v2b)^2)-(1/2(ma+mb)(v1a+v1b)^2) = 190J wrong

with other combos I've gotten as high as 1490J which was also wrong.

any help is greatly appreciated.
 
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  • #2
You know the speed of each car before and after the collision. So just calculate the total kinetic energy before and after and compare. Calculate the KE of each car separately, then add them up.
 
  • #3
okay, so:

K1a = 1/2(1850)(1.60)^2 = 2368J
K1b = 1/2(1450)(1.10)^2 = 877J

K2a = 1/2(1850)(.270)^2 = 67J
K2b = 1/2(1450)(.597)^2 = 258J

deltaK = (2368+877)-(67+258) = 2920J?
 
  • #4
Looks good to me. (Assuming you calculated the final speed of the lighter car correctly; I didn't check.)

Edit: I just confirmed your speed calculation.
 
Last edited:
  • #5
Doc Al said:
Looks good to me. (Assuming you calculated the final speed of the lighter car correctly; I didn't check.)

Edit: I just confirmed your speed calculation.

thanks, yeah I know part A is right for sure (masteringphysics)

thanks again Doc Al!
 
  • #6


As i understood it, the two cars collided with an elastic form of collision. Therefore momentum and kinetic energy is conserved (same before and after the collision). How come that in the computation of the two kinetic energy before and after (the one you presented with us) are not equal (3245 J before collision and 325 J after collision)? I thought they will be equal. This is confusing for me.

You just showed combined kinetic energy.
Please help me. Explain it in detail.
 
  • #7


samelliz said:
As i understood it, the two cars collided with an elastic form of collision. Therefore momentum and kinetic energy is conserved (same before and after the collision).
No, the collision is not elastic. Only momentum is conserved. You have enough information to solve for the final speeds using only conservation of momentum (that was part a).

(Realize that you are responding to a post that is over three years old.)
 

Related to Change in kinetic energy in a 2-car collision

1. How is kinetic energy defined?

Kinetic energy is the energy that an object possesses due to its motion. It is calculated by the equation KE = 1/2 * m * v^2, where m is the mass of the object and v is its velocity.

2. How is kinetic energy affected in a 2-car collision?

In a 2-car collision, the kinetic energy of both cars is affected. The total kinetic energy of the two cars before the collision is equal to the sum of their individual kinetic energies. After the collision, some of this kinetic energy is transferred to other forms of energy, such as sound and heat, while the remaining energy is retained by the cars in the form of kinetic energy.

3. Does the mass of the cars affect the change in kinetic energy in a collision?

Yes, the mass of the cars does affect the change in kinetic energy in a collision. The higher the mass of the cars, the greater the amount of kinetic energy they possess. This means that in a collision between two cars with different masses, the car with a higher mass will experience a smaller change in kinetic energy compared to the car with a lower mass.

4. What is the relationship between velocity and change in kinetic energy in a collision?

The relationship between velocity and change in kinetic energy in a collision is direct. This means that the faster the cars are moving, the greater the change in kinetic energy will be during the collision. This is because velocity is a key component in the calculation of kinetic energy, and a higher velocity will result in a higher amount of kinetic energy.

5. How is the conservation of energy applied in a 2-car collision?

The conservation of energy states that energy cannot be created or destroyed, only transferred from one form to another. In a 2-car collision, the total amount of kinetic energy before and after the collision remains the same, as long as no external forces are present. This means that the loss of kinetic energy in the collision is equal to the gain of other forms of energy, such as sound and heat.

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