Calculating Momentum A Physics Problem With Solution
In the realm of physics, momentum stands as a fundamental concept, crucial for understanding the motion of objects. It quantifies the inertia of a moving object, essentially measuring how difficult it is to change its state of motion. This article delves into the concept of momentum through a practical problem, guiding you step-by-step to calculate the momentum of a system. We will explore the key definitions, the formula for momentum calculation, and apply these principles to solve a real-world scenario. So, let's embark on this physics journey and unravel the mysteries of momentum!
To effectively tackle the problem at hand, it's crucial to first grasp the underlying principles of momentum. Momentum, denoted by the symbol p, is a vector quantity, meaning it possesses both magnitude and direction. It is defined as the product of an object's mass (m) and its velocity (v). Mathematically, this is expressed as:
p = m * v
Where:
- p represents momentum (typically measured in kilogram meters per second, kg m/s)
- m represents mass (typically measured in kilograms, kg)
- v represents velocity (typically measured in meters per second, m/s)
The formula reveals that momentum is directly proportional to both mass and velocity. This implies that a heavier object moving at the same velocity will have greater momentum than a lighter one. Similarly, an object moving at a higher velocity will possess more momentum than the same object moving slower. Understanding this relationship is key to solving momentum-related problems.
Now, let's consider the specific problem we aim to solve. The scenario involves Rita, who is riding her bicycle. We are given the following information:
- Mass of the bicycle (m_bike) = 7.0 kilograms
- Velocity of Rita and the bicycle (v) = 15 meters/second
- Mass of Rita (m_Rita) = 42 kilograms
The question asks us to determine the total momentum of Rita and the bicycle system. To solve this, we need to consider the combined mass of Rita and the bicycle and then apply the momentum formula. This problem highlights the importance of considering the entire system when calculating momentum, especially when multiple objects are involved.
To accurately calculate the momentum in this scenario, we will follow a structured approach, breaking the problem down into manageable steps:
Step 1: Calculate the total mass of the system.
The system consists of Rita and her bicycle. Therefore, we need to add their masses to find the total mass (m_total):
m_total = m_Rita + m_bike
m_total = 42 kg + 7.0 kg
m_total = 49 kg
This step is crucial as it ensures we account for the inertia of both Rita and the bicycle when calculating the overall momentum.
Step 2: Apply the momentum formula.
Now that we have the total mass and the velocity, we can use the momentum formula:
p = m_total * v
p = 49 kg * 15 m/s
p = 735 kg m/s
This calculation gives us the magnitude of the momentum. Since velocity is a vector quantity, momentum is also a vector, and its direction is the same as the velocity. In this case, we are primarily concerned with the magnitude of the momentum.
Step 3: Express the answer in scientific notation (if necessary).
The calculated momentum is 735 kg m/s. The answer choices are provided in scientific notation, so we should convert our result accordingly.
735 = 7.35 x 10^2
Rounding to two significant figures (as in the given options), we get:
7.4 x 10^2 kg m/s
This step ensures our answer is in the correct format for comparison with the provided options. It also demonstrates a practical application of scientific notation, which is commonly used in physics to express very large or very small quantities.
Having calculated the momentum, we now need to compare our result with the given answer choices to identify the correct one. The options are:
- A. kilogram meters/second
- B. kilogram meters/second
- C. kilogram meters/second
- D. kilogram meters/second
Our calculated momentum is 7.4 x 10^2 kg m/s, which exactly matches option D. Therefore, option D is the correct answer. This step highlights the importance of careful calculation and comparison to ensure the final answer is accurate.
Beyond the numerical calculation, it's important to reflect on what the momentum value signifies in this context. The momentum of 7.4 x 10^2 kg m/s represents the inertia of Rita and her bicycle as they move together. It indicates the force required to bring them to a stop or change their direction. A higher momentum value implies a greater resistance to changes in motion.
In real-world scenarios, understanding momentum is crucial in various applications, such as designing vehicles, analyzing collisions, and even in sports. For instance, the momentum of a football player affects the impact of a tackle, and the momentum of a car influences the severity of a collision. This broader perspective emphasizes the practical relevance of the concept of momentum in our daily lives.
In conclusion, we have successfully calculated the momentum of Rita and her bicycle by applying the fundamental principles of physics. By carefully considering the system's total mass and velocity, we arrived at the correct answer: 7.4 x 10^2 kilogram meters/second. This exercise not only reinforces our understanding of the momentum formula but also highlights the importance of a systematic approach to problem-solving in physics.
Furthermore, we have explored the significance of momentum as a measure of an object's inertia and its relevance in real-world applications. This holistic understanding underscores the value of physics in explaining and predicting the motion of objects around us. As you continue your exploration of physics, remember that momentum is a cornerstone concept that will underpin your understanding of more advanced topics.
The correct answer is D. kilogram meters/second
