A 0.02 kg-lead bullet traveling 200 m/s strikes an armor plate and comes to a stop. If all of it's energy is converted to heat that it absorbs, what is the temperature change?
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To determine the temperature change, we need to use the principle of conservation of energy. The kinetic energy of the bullet is converted into heat energy when it comes to a stop.
First, let's calculate the initial kinetic energy (KE) of the bullet using the formula:
KE = (1/2) * m * v^2
where:
m = mass of the bullet = 0.02 kg
v = velocity of the bullet = 200 m/s
Plugging in the values:
KE = (1/2) * 0.02 kg * (200 m/s)^2
KE = 400 J
The kinetic energy is 400 Joules.
Next, according to the principle of conservation of energy, this energy is converted into heat. We can assume that all the energy is absorbed by the bullet and leads to an increase in its temperature.
Now we need to consider the specific heat capacity (c) of lead, which represents the amount of heat energy required to raise the temperature of a given amount of substance by 1 degree Celsius. The specific heat capacity of lead is approximately 130 J/kg°C.
To calculate the temperature change (∆T), we can use the formula:
∆T = KE / (m * c)
where:
∆T = temperature change
KE = kinetic energy
m = mass of the bullet
c = specific heat capacity of lead
Plugging in the values:
∆T = 400 J / (0.02 kg * 130 J/kg°C)
∆T ≈ 153.84 °C
Therefore, the temperature change of the lead bullet after it comes to a stop is approximately 153.84 °C.