Heat and Kinetic Energy Question

[a_narain]

Homework Statement

Two cars collide as both are traveling at 90km/hr. What is the increase in temperature of the wrecks, assuming that the cars have c = 447 joules/kelvin.

Homework Equations

Q= mc(change in T)

The Attempt at a Solution

I found the joules of kinetic energy equal to 625 joules * mass of car (25 m/s speed = 625/2 joules of KE per car X two cars).
I then divided that by 447 for the c value, to get 1.4 K. But the answer is not correct?

 

[LowlyPion]

Homework Statement

Two cars collide as both are traveling at 90km/hr. What is the increase in temperature of the wrecks, assuming that the cars have c = 447 joules/kelvin.

Homework Equations

Q= mc(change in T)

The Attempt at a Solution

I found the joules of kinetic energy equal to 625 joules * mass of car (25 m/s speed = 625/2 joules of KE per car X two cars).
I then divided that by 447 for the c value, to get 1.4 K. But the answer is not correct?

Half of that would be correct though wouldn't it?

Don't you have to consider the total heat into the total mass?

 

[nlightner]

I would like to clarify some things about the given information. Firstly, it is important to specify the units for speed, as 90 km/hr is not a unit of speed in the SI system. Assuming that the speed is 25 m/s, the calculation for the kinetic energy of each car is correct. However, the equation Q=mc(change in T) is used to calculate the heat transferred, not the change in temperature. In this case, the heat transferred would be equal to the kinetic energy of both cars combined, which is 1250 joules. To calculate the change in temperature, we would need to divide this value by the total mass of both cars and the specific heat capacity, which is given as 447 joules/kelvin. This would give a change in temperature of approximately 0.003 K. It is important to note that this is a very small change in temperature and may not be noticeable. Additionally, this calculation assumes that all of the kinetic energy is converted into heat, which may not be the case in a real collision. Other forms of energy, such as sound and deformation of the cars, may also be produced.