A 3.00 g lead bullet traveling at 640 m/s strikes a target, converting its kinetic energy into thermal energy. It's initial temperature is 40.0°C.

Find the available kinetic energy of the bullet.
Find the heat required to melt the bullet.

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To find the available kinetic energy of the bullet, we will use the formula:

Kinetic Energy (K.E.) = 1/2 * mass * velocity^2

Given:
Mass of the bullet (m) = 3.00 g = 0.003 kg
Velocity of the bullet (v) = 640 m/s

Using the formula, we can calculate the kinetic energy:

K.E. = 1/2 * 0.003 kg * (640 m/s)^2
= 1/2 * 0.003 kg * 409600 m^2/s^2
= 614.4 J

Therefore, the available kinetic energy of the bullet is 614.4 Joules.

To find the heat required to melt the bullet, we need to determine the amount of energy required to raise the temperature of the bullet from its initial temperature to its melting point, and then the energy required to actually melt it.

First, we will calculate the energy required to raise the temperature of the bullet using the formula:

Q = m * c * ΔT

Where:
m = mass of the bullet = 3.00 g = 0.003 kg
c = specific heat capacity of lead = 130 J/kg°C
ΔT = change in temperature = final temperature - initial temperature

Given:
Initial temperature (T1) = 40.0°C
Final temperature (T2) = melting point of lead = 327.5°C

ΔT = T2 - T1
= 327.5°C - 40.0°C
= 287.5°C

Now, let's calculate the heat required to raise the temperature of the bullet:

Q1 = 0.003 kg * 130 J/kg°C * 287.5°C
= 112.125 J

Next, the energy required to melt the bullet can be calculated using the formula:

Q2 = m * L

Where:
L = latent heat of fusion of lead (amount of heat required to convert 1 kg of lead from solid to liquid) = 23,000 J/kg

Given:
Mass of the bullet (m) = 0.003 kg

Now, let's calculate the heat required to melt the bullet:

Q2 = 0.003 kg * 23,000 J/kg
= 69 J

Finally, to find the total heat required to melt the bullet, we add the two quantities of heat calculated earlier:

Total heat required = Q1 + Q2
= 112.125 J + 69 J
= 181.125 J

Therefore, the total heat required to melt the bullet is 181.125 Joules.