Final answer:
The mechanical energy dissipated in the collision is 200 J. The temperature increase of the system due to the collision is 40.03 K.
Step-by-step explanation:
To calculate the mechanical energy dissipated in the collision, we need to find the kinetic energy before and after the collision. The kinetic energy before the collision is given by (1/2) * m * v^2, where m is the mass of the bullet and v is its velocity. Substituting the values, we get (1/2) * 0.01 kg * (200 m/s)^2 = 200 J. After the collision, the bullet and the pendulum bob together have a new combined mass of 2.01 kg (10 g + 2000 g). The velocity of the combined system is zero since the bullet embeds in the bob. Therefore, the mechanical energy dissipated in the collision is the difference in kinetic energy before and after the collision, which is 200 J - 0 J = 200 J.
To calculate the temperature increase of the system, we can use the equation Q = mcᵥΔT, where Q is the heat transferred, m is the mass of the system, cᵥ is the specific heat capacity at constant volume, and ΔT is the change in temperature. Rearranging the equation, we have ΔT = Q / (mcᵥ). Substituting the values, we get ΔT = 200 J / (0.2 kg * 3 * 8.31 J/mol·K) = 40.03 K. Therefore, the temperature increase of the system due to the collision is 40.03 K.