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Momentum is a key physical quantity that measures the motion of an object. It is defined as the product of an object's mass and its velocity. The unit of momentum in the International System (SI) is kilogram meter per second (kg·m/s). The formula for calculating linear momentum is:
\[ p = m \times v \]
where:

• \( p \) is the momentum,
• \( m \) is the mass of the object, and
• \( v \) is the velocity of the object.

This formula tells us that the momentum of an object increases as its mass or velocity increases. Understanding this helps us to solve problems relating to objects in motion, such as particles, vehicles, and celestial bodies. Now, let's explore specific examples of momentum.

In physics, protons are fundamental subatomic particles with a positive charge. They have a very small mass on the atomic scale. Therefore, calculating the momentum of a proton involves small numbers. For example, when a proton with a mass of \(1.67 \times 10^{-27}\) kg moves at a speed of \(5.00 \times 10^{6}\) m/s, its momentum \( p \) can be calculated as:
\[ p = (1.67 \times 10^{-27} \text{ kg}) \times (5.00 \times 10^{6} \text{ m/s}) \]
Evaluating the product, we obtain a momentum of \(8.35 \times 10^{-21}\) kg·m/s. This small value reflects the tiny mass of the proton. It's important for understanding behaviors at the atomic scale and plays a critical role in areas like particle physics.

Bullets, with their relatively small mass, achieve high values of momentum due to their high speeds. To compute the momentum of a bullet weighing 15.0 grams moving at 300 m/s, we need to first convert the mass to kilograms, yielding 0.015 kg. Using the same momentum formula, we compute:
\[ p = (0.015 \text{ kg}) \times (300 \text{ m/s}) \]
The resulting momentum is \(4.5\) kg·m/s. This illustrates how even small objects can have significant momentum due to their velocity. In practical terms, understanding bullet momentum is crucial in fields such as ballistics, which explore the dynamics of projectiles.

The Earth, despite moving relatively slowly compared to subatomic particles, possesses immense momentum due to its enormous mass. With a massive weight of \(5.98 \times 10^{24}\) kg and moving through space at an impressive speed of \(2.98 \times 10^{4}\) m/s, Earth's momentum can be calculated as:
\[ p = (5.98 \times 10^{24} \text{ kg}) \times (2.98 \times 10^{4} \text{ m/s}) \]
This calculation results in a colossal momentum of about \(1.78 \times 10^{29}\) kg·m/s. This massive momentum contributes significantly to the gravitational interactions and dynamics observed in our solar system, impacting everything from orbital stability to the effects of gravitational pulls.