What is the Temperature Increase of Cars Colliding at 80 km/hr?

[Flip18064]

Homework Statement

Two cars collide head on while each is traveling at 80 km/hr. Suppose all their kinetic energy is transformed into the thermal energy of the wrecks. What is the temperature increase of each car? (Assume each car's specific heat is that of iron)

Homework Equations

K = .5mv^2
Q = cm(delta T)
iron specific heat = .449 J/(g*K)

The Attempt at a Solution

K = 2(.5m(22.2)^2) = 492.8m

(converted 80 km/hr to m/s)

Q = 492.8m = (.449)(2m)(delta T)
delta T = 548.8 KWhich is the wrong answer. I don't know what i am doing wrong. Can someone please help me. Thanks

 

[Flip18064]

Got, it. Just needed to convert iron specific heat from J/(g*K) to J/(kg*K), so delta T is just .549

 

[nlightner]

I would like to point out that the equations and values used in this attempt at a solution are correct. However, there are some assumptions that need to be clarified.

Firstly, the specific heat of iron used in this problem is for solid iron, not for a car which is made up of various materials such as metal, plastic, and rubber. Therefore, the specific heat of the car would be different and would need to be determined using the specific heat values of the individual materials.

Secondly, the assumption that all of the kinetic energy of the cars is transformed into thermal energy is not entirely accurate. Some of the energy would also be dissipated as sound and deformation of the cars. This would affect the final temperature increase of the cars.

Lastly, temperature is a macroscopic property and cannot be accurately determined for individual objects in a collision. The temperature increase would depend on the mass and composition of the cars, as well as the efficiency of energy transfer during the collision. Therefore, the answer obtained may not be entirely accurate.

In conclusion, while the attempt at the solution is correct, there are some assumptions and limitations that need to be considered when solving this problem. It is important to always be critical and aware of these factors when conducting scientific calculations.