Grigoriy S. answered • 12/03/21

AP Physics / Math Expert Teacher With 40 Years of Proven Success

We will be using the law of conservation of energy. The energy released by bullet will be equal to energy that required to melt ice.

The bullet was moving in the beginning; as a result it had kinetic energy *K = ½( m*_{1}* v*^{2}** )**,

where m_{1} = 3.29 x 10^{-3} kg – mass of the bullet,

v = 229 m/s – its speed.

The temperature of the bullet is t_{1 }= 31. 5 °C. The melting point of ice is t_{2} = 0 °C. Hence, while cooling to this temperature it will give the ice extra heat *Q*_{1}* = c∙m*_{1}*∙( t*_{1}* – t*_{2}** )**,

here c = 900 J/(kg∙°C) - specific heat of aluminum.

The total amount of energy received from the bullet by ice is *K + Q*_{1}. This energy will be used to melt some ice. Ice required heat *Q*_{2}* = L∙m*_{2} to melt, where

L = 3.34 x 10^{ 5} J/kg – heat of fusion of ice.

Now we can write

½( m_{1} v^{2}) + c∙m_{1}∙( t_{1} – t_{2}) = L∙m_{2} .

From this equation

m_{2} = ( (½( m_{1}v^{2}) + c∙m_{1}∙( t_{1} – t_{2}) ) / L

Now you need to put all values of variables in this equation and get the answer.

If my calculator is not wrong, the answer is 5.3 x 10 ^{-,4} kg or **0.53 g**.