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Bullet stops and heats

  1. Oct 16, 2014 #1
    1. The problem statement, all variables and given/known data
    A lead bullet flies at 350[m/s], hits and stops. if no heat escapes, how much will it's temperature rise

    2. Relevant equations
    ##Q[cal]=m\cdot c\cdot \Delta t##
    Specific heat of lead: c=0.031

    3. The attempt at a solution
    The kinetic energy: [itex]E=\frac{1}{2}mv^2=\frac{1}{2}m\cdot 350^2=m\cdot 61,250[Joule][/itex]
    ##\frac{61,250}{4.186}=14,632[cal]\rightarrow E=m\cdot 14,632[cal]##
    ##Q=E=m\cdot 14,632[cal]=m\cdot 0.031\cdot \Delta T##
    And it gets a huge temperature
  2. jcsd
  3. Oct 16, 2014 #2


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    Homework Helper

    The energy is in joules if m is in kg-s. At the same time you use cal/(g C°) for specific heat. So the m-s on both sides of the last equation are not the same, it is in kg-s on the left side and grams on the right side. Better to use the SI units.

  4. Oct 16, 2014 #3
    The kinetic energy: [itex]E=\frac{1}{2}mv^2=\frac{1}{2}m\cdot 350^2=m\cdot 61,250[Joule][/itex]
    ##\frac{61,250}{4,186}=14.6[kcal]\rightarrow E=m\cdot 14.6[kcal]##
    The specific heat doesn't change it's value, 0.031, because of the unit change:
    ##Q=E=m\cdot 14.6[kcal]=m\cdot 0.031\left[\frac{kcal}{kg\cdot k^0}\right] \cdot \Delta T\rightarrow Delta T=472^0##
    Is that logical? the melting point of lead is 3270
    Last edited: Oct 16, 2014
  5. Oct 16, 2014 #4


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    May I make a suggestion? One should never use, in decimal fractions, three figures. Thus, the risk of confusion is easily avoided.

    For example, when converting to SI units the sp. heat of lead, I would write 0,0310 cal/g*ºC x 4,1860 Joule/cal = 0,1298 J/g*ºC = 129,8 J/kg*K

    A comment: I went to school in a 'decimal point country', and later moved to a 'decimal comma country'... I have always avoided three decimals, and even use the elevated comma to write them... 129'8 is, for example, my usual way of writing decimals... Not unusual in Spain, even if this is a 'decimal comma country'...

    I see that the problem has been solved. So, I believe that I can now write down my solution, using SI units throughout:

    Delta T = Energy of the bullet/specific heat * mass

    As the kinetic energy of a bullet of m mass at 350 m/s is 61250m Joule, we have:

    Delta T = 61250m Joule/((129,8 J/Kg*K )* m) = 61250/129,8 = 472 K of rise in temperature...
    Last edited: Oct 16, 2014
  6. Oct 16, 2014 #5
    The kinetic energy: [itex]E=\frac{1}{2}mv^2=\frac{1}{2}m\cdot 350^2=m\cdot 61250[Joule][/itex]
    ##Q=E=m\cdot 61250[kcal]=m\cdot 129.8\left[\frac{Joule}{kg\cdot k^0}\right] \cdot \Delta T\rightarrow Delta T=472^0##
    The same high result, does the bullet melt??
  7. Oct 16, 2014 #6


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    That's not relevant. This is a physics problem... In real life, it is difficult that the whole of the kinetic energy resulting from the strike may be converted in heating the bullet, as the target is usually deformed permanently and heats up somewhat, the bullet may permanently deform or break, (something that needs energy) it may recoil, or the pieces may recoil, taking away part of the kinetic energy, and that may result in other permanent deformations elsewhere, and in an increase of the temperature of the surroundings...
  8. Oct 16, 2014 #7


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    I think it's logical.
    For a real bullet most of the energy is spent blowing someone's skull apart ?:) Which probably takes a fair amount of energy, which if converted to heat would be significant.

    It's always good to check whether your answer makes some sort of physical sense. But in this case, as NTW points out it's hard to do.
  9. Oct 16, 2014 #8


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    Homework Helper

    Do not expect a problem maker to think of everything... :) The bullet stops in such a short time that it can not melt yet. It gets hot, it starts to melt and starts to give heat to the surroundings.
    By the way, higher speed bullets are made of some alloy, which melts at higher temperature.

  10. Oct 16, 2014 #9
    Thank you everybody, i won't mess with bullets...
  11. Oct 16, 2014 #10
    The bullet gets heat, but target gets heat too
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