Thermodynamic with inelastic collision

[physikx]

Homework Statement

[/B]A bullet traveling at 100 m/s strikes the wall inelastically. It is observed that the bullet's temperature rises by 10 Kelvin due to the collision. Find the specific heat capacity of the bullet if all of the bullet's energy goes into heat.

Homework Equations

ΔQ=mcΔT
KE=1/2mv^2

The Attempt at a Solution

I tried to solve this problem in different ways, but I was not able to do anything without the mass. I know I might be approaching in the wrong way, but I figured if I can determine its kinetic energy lost then I can use that for the heat lost. From there I would figure out the heat capacity of the bullet; that is not feasible though because mass is not given. I just need some guidance on how to approach the problem, I am more than happy to solve it myself after that. Thank you!

 

[ehild]

Homework Equations

ΔQ=mcΔT
KE=1/2mv^2

The Attempt at a Solution

I tried to solve this problem in different ways, but I was not able to do anything without the mass.

How would you solve the problem if you knew that the mass is 0.1 kg?

ehild

 

[physikx]

Would this be right ehild?

KE=1/2mv^2
KE=1/2(.1)(100)^2=500J

ΔQ=500J
m=.1
ΔT=10K

ΔQ=mcΔT
500J=(.1kg)c(10k)
c=500J/Kg*k

 

[ehild]

What happens if m=0.012345 kg? Do not evaluate the KE, just do what you did before.

ehild.

 

[physikx]

What happens if m=0.012345 kg? Do not evaluate the KE, just do what you did before.

I am not sure if I did anything before evaluating the kinetic energy. I am assuming the mass is not a limiting factor, and that energy change is actually indicated by the temperature change of 10 kelvin? Now, I just tried that mass and a couple of others and I still got the same answer. Does mass not matter because 1/2v^2=cΔT. Thank you for your insight!

 

[physikx]

c=v^2/(2ΔT)

I believe this is the answer. If it is, thanks for the indescribable genius -answering my question with knowledge loaded question! I hope I am not getting ahead of myself.

 

[ehild]

Now, I just tried that mass and a couple of others and I still got the same answer. Does mass not matter because 1/2v^2=cΔT. Thank you for your insight!

You see, the mass cancels, as it both sides of the equation is "something multiplied by mass". It happens quite often, so try to solve problems symbolically, as some variables can just cancel. Plug in data and evaluate at the end.


ehild

 

[ehild]

c=v^2/(2ΔT)

I believe this is the answer. If it is, thanks for the indescribable genius -answering my question with knowledge loaded question! I hope I am not getting ahead of myself.

Yes, it is the answer, the general formula which applies for every velocity and temperature change. You are a genius

ehild

 

[physikx]

Thanks for the guidance. I will definitely always keep that in the back of my mind when I am solving problems. Physics takes a great amount of practice, but it is worth it because it is real knowledge! Thanks again... I am still impressed! :)

 

[ehild]

Thanks for the guidance. I will definitely always keep that in the back of my mind when I am solving problems. Physics takes a great amount of practice, but it is worth it because it is real knowledge! Thanks again... I am still impressed! :)

You are a good student and I am sure you will be going well with Physics. Yes, you need lot of practice, and practice also helps to discover new things. That is the beauty of both Physics and Maths that you can find out laws by yourself, starting out from some basic axioms, like Newton's Laws or the three axioms of Thermodynamics.

ehild

 

[physikx]

Thanks again for your inspiring words child, they most definitely resonate in my mind. I hope to get to the level of knowledge in physics that allows me to help other folks on here, your work is truly inspiring. I appreciate your time and knowledge with my regard to the PF team, you guys are the true heroes!