A 10.0 g iron bullet with a speed of 4.00 ×10^2 m / s and a temperature of 20.0^∘ C is stopped i

step 1 Solving part A of this problem, so I will use the formula MC del T is equal to half mv square. S

A 10.0 g iron bullet with a speed of 4.00 ×10^2 m / s and a...

A $10.0 \mathrm{g}$ iron bullet with a speed of $4.00 \times 10^{2} \mathrm{m} / \mathrm{s}$ and a temperature of $20.0^{\circ} \mathrm{C}$ is stopped in a $0.500 \mathrm{kg}$ block of wood, also at $20.0^{\circ} \mathrm{C},$ which is fixed in place. (a) At first all of the bullet's kinetic energy goes into the internal energy of the bullet. Calculate the temperature increase of the bullet. (b) After a short time the bullet and the block come to the same temperature $T$. Calculate $T$, assuming no heat is lost to the environment.

A $10.0 \mathrm{g}$ iron bullet with a speed of $4.00 \times 10^{2} \mathrm{m} / \mathrm{s}$ and a temperature of $20.0^{\circ} \mathrm{C}$ is stopped in a $0.500 \mathrm{kg}$ block of wood, also at $20.0^{\circ} \mathrm{C},$ which is fixed in place. (a) At first all of the bullet's kinetic energy goes into the internal energy of the bullet. Calculate the temperature increase of the bullet.
(b) After a short time the bullet and the block come to the same temperature $T$. Calculate $T$, assuming no heat is lost to the environment.

Key Concepts

Specific Heat Capacity

Specific heat capacity is a property of a material that indicates how much energy is needed to raise the temperature of a unit mass of the substance by one degree Celsius. This concept is essential in calculating the temperature change of the bullet and the block when energy is added or removed.

Heat Transfer and Thermal Equilibrium

Heat transfer involves the flow of thermal energy from one object to another due to a temperature difference. In this problem, after the bullet’s kinetic energy is converted to internal energy and the bullet and block come into contact, heat flows until they reach thermal equilibrium, meaning both the bullet and block end up at the same final temperature.

Kinetic Energy

This is the energy possessed by an object due to its motion and is given by the formula ½mv². In the context of the problem, the bullet's kinetic energy is initially very high due to its speed, and this energy is converted into internal energy (thermal energy) when the bullet is stopped by the block.

Conservation of Energy

This principle states that energy cannot be created or destroyed, only converted from one form to another. Here, the bullet’s kinetic energy is completely transformed into thermal energy within the bullet and later distributed between the bullet and the block, while no energy is lost to the surroundings.

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