A bit of space debris penetrates the hull of a spaceship...

A bit of space debris penetrates the hull of a spaceship traversing the asteroid belt and comes to rest in a container of water that was at $20.0^{\circ} \mathrm{C}$ before being hit. The mass of the debris is $1.0 \mathrm{g}$ and the mass of the water is $1.0 \mathrm{kg} .$ If the space rock traveled at $8.4 \times 10^{3} \mathrm{m} / \mathrm{s}$ with respect to the spaceship and if all of its kinetic energy is used to heat the water, what is the final temperature of the water?

Key Concepts

Kinetic Energy

Kinetic energy is the energy that an object possesses due to its motion. It is calculated using the formula KE = ½ mv², where m is the mass and v is the velocity of the object. This concept is crucial in understanding how the initial energy of a moving object can be transferred to another system or medium during an interaction.

Conservation of Energy

The principle of conservation of energy states that energy cannot be created or destroyed, only transformed from one form to another. In scenarios where an object transfers its kinetic energy to another system, the total energy before and after the interaction remains constant, allowing the prediction of system changes such as temperature increases.

Specific Heat Capacity

Specific heat capacity is a property of a substance that indicates the amount of energy required to raise the temperature of a unit mass of the substance by one degree Celsius. This concept is essential when calculating how much a given amount of energy will increase the temperature of a substance, such as water.

Calorimetry

Calorimetry is the science of measuring the amount of heat absorbed or released during a chemical or physical process. It involves applying the principle that the energy transferred as heat in a system can be related to changes in temperature, making it possible to determine the final temperature of a substance after energy is added.

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