Problem 2 - Applied Physics

Question

Find the momentum of each object. \(\quad m=5.00 \mathrm{~kg}, v=90.0 \mathrm{~m} / \mathrm{s}\)

Step-by-Step Solution

Answer

Momentum is 450.0 kg·m/s.

Step 1: Understanding the Concept

Momentum is a measure of the motion of an object and is calculated using the formula: \( p = m imes v \), where \( p \) is the momentum, \( m \) is the mass of the object, and \( v \) is the velocity of the object.

Step 2: Identifying the Given Variables

Identify the given values from the problem. Here, the mass \( m \) is given as \( 5.00 \mathrm{~kg} \) and the velocity \( v \) is given as \( 90.0 \mathrm{~m/s} \). We will use these values in the formula to calculate momentum.

Step 3: Substituting the Values into the Formula

Substitute the given values into the momentum formula. Thus, we have:\[ p = 5.00 \mathrm{~kg} \times 90.0 \mathrm{~m/s} \]

Step 4: Calculating the Result

Perform the multiplication to find the momentum:\[ p = 5.00 \times 90.0 = 450.0 \mathrm{~kg} \cdot \mathrm{m/s} \]

Step 5: Conclusion

The momentum of the object is \( 450.0 \mathrm{~kg} \cdot \mathrm{m/s} \). This value represents the quantity of motion the object possesses at the given mass and velocity.

Key Concepts

Mass and Velocity

In physics, two critical parameters that define how an object moves are mass and velocity. Understanding these parameters gives a deeper insight into momentum calculation. Let's break it down:

• Mass: This is the amount of matter present in an object. It's measured in kilograms (kg) and tells us about the object's inertia, or what resists changes to its motion.
• Velocity: Velocity is a vector quantity that includes both the speed and direction of an object's movement. Measured in meters per second (m/s), it indicates not just how fast an object is moving, but also in which direction.

In our exercise, the mass is 5.00 kg and the velocity is 90.0 m/s. These values are crucial because the momentum of an object depends directly on both mass and velocity. This interplay is central to why an object with a larger mass or higher velocity will possess greater momentum.

Momentum Formula

The momentum formula is a simple yet powerful tool in physics that allows us to quantify the motion of an object. The formula is written as:

\[ p = m \times v \]

Where:

• \( p \) represents momentum.
• \( m \) is the mass of the object (in kg).
• \( v \) is the velocity of the object (in m/s).

Momentum is a vector quantity, meaning it has both magnitude and direction. The direction of the momentum vector is the same as the direction of velocity. The momentum formula helps us understand how objects move and interact. For instance, in a collision, the total momentum before and after should remain constant, which is a reflection of the conservation of momentum principle.

In solving the exercise, by applying \( p = 5.00 \times 90.0 \), we determine the momentum as 450.0 kg·m/s, indicating the object's total motion in a specific direction.

Physics Problem Solving

Breaking down physics problems is essential for understanding and mastering the concepts. Here's a structured approach that you can use for solving problems related to mass, velocity, and momentum:

• Identify Known Values: Start by listing what you know. For instance, in the exercise, we knew the mass (5.00 kg) and the velocity (90.0 m/s).
• Identify What is Asked: Clearly understand what you need to find. The question required calculating momentum.
• Choose the Right Formula: Select the appropriate formula. Here, it was \( p = m \times v \).
• Substitute and Solve: Insert the known values into the formula and perform the necessary calculations. In this case, multiplying mass and velocity gave us the momentum.
• Verify Your Answer: Reflect on the answer to ensure it makes sense contextually. It should satisfy the physical intuition of the problem space.

This structured method aids in clear thinking and reduces the chances of errors. By practicing these steps, students can efficiently tackle a wide range of physics problems, gaining confidence and fluency in the subject.