Calculating Temperature Change of a Lead Bullet on Impact

[porschedriver192]

A 4.2 g lead bullet moving at 260 m/s strikes a steel plate and stops. If all its kinetic energy is converted to thermal energy and none leaves the bullet, what is its temperature change?
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I don't even know what formula to use or how to start.

I could get force, by multiplying the mass x accel, but I don't know how to relate that to temperature.
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Thanks.

 

[Sirus]

You need to think in terms of energy here. Can you find the kinetic energy of the bullet before it strikes the plate? Now you need to have the specific heat capacity of the bullet, so you can use
Q=mc\Delta T
where Q would be the energy (converted from kinetic to thermal), and c the specific heat capacity. From there you can find the change in temperature.

 

[porschedriver192]

Thanks for the reply...ok the spec. heat of the lead bullet is 128 kg/J*C

how do I convert the Kinetic Energy into Thermal?

So far I have:

Q = (m)(c)(change in temp)

? = (.0042)(128)(x)

I don't know how to find Q, so then I can solve for x.

Thanks.

 

[Sirus]

Q is basically the energy change of the system. You don't have to "convert" kinetic to thermal. Once you have kinetic, the question tells you all of that is converted to thermal, so you can sub that into the second equation as thermal (heat) energy.