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.

(a)Find the available kinetic energy of the bullet.(J)
(b)Find the heat required to melt the bullet.(J)

KE=1/2 massbullet* velocity^2

heat required to melt=heat required to change temp to melting poing+heat to change lead to liquid
= mass*specifHeatLead*(Tm-40)+mass*HeatfusionLead

look up the specifice heat of lead, the temperature of melting lead, and finally the heat of fusion for lead.

bullet mass: M = 3.00g

initial velocity: V0 = 640m/s
initial temperature: T0 = 313.15K
final velocity: V1 = 0m/s
melting point of Lead: T2 = 600.61K
specific heat of lead: C = 0.128J/g/K
latent heat of melting: L = 22.4J/g

(a)Find the available kinetic energy of the bullet.(J)
∆E1 = (1/2)(M)(V1^2-V0^2)

(b) Find the heat required to melt the bullet.(J)
∆E2 = M C (T2-T0) + M L

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To calculate the available kinetic energy of the bullet, we can use the formula:

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

(a) Available kinetic energy of the bullet:
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:

Kinetic Energy = (1/2) * 0.003 kg * (640 m/s)^2
= 0.5 * 0.003 kg * (409600 m^2/s^2)
= 614.4 J

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

(b) To find the heat required to melt the bullet, we need to know the specific heat capacity (c) of lead and the heat of fusion (ΔH_fusion) of lead.

The specific heat capacity of lead (c) is approximately 130 J/kg°C.
The heat of fusion of lead (ΔH_fusion) is approximately 24,500 J/kg.

To calculate the heat required to melt the bullet, we can use the formula:

Heat = mass * (change in temperature + latent heat of fusion)

The change in temperature (ΔT) is the final temperature (T_f) minus the initial temperature (T_i). Since the bullet is melting, the final temperature will be the melting point of lead, which is approximately 327°C.

Therefore, ΔT = T_f - T_i = 327°C - 40.0°C = 287°C = 287 K.

The mass of the bullet (m) is given as 3.00 g = 0.003 kg.

Using the formula, we can calculate:

Heat = 0.003 kg * (287 K + (24500 J/kg) / (130 J/kg°C))
= 0.003 kg * (287 K + 188.46°C)
= 0.003 kg * (475.46 K)
= 1.42638 J

Therefore, the heat required to melt the bullet is approximately 1.43 J.