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Chapter 2: Problem 67

A bullet of mass \(4 \mathrm{~g}\) moving with a velocity of \(400 \mathrm{~m} / \mathrm{s}\) will have \begin{tabular}{|l|l} \hline Select... & v \\ \hline greater \\ \hline less \\ \hline \end{tabular} momentum than a baseball of mass \(150 \mathrm{~g}\) thrown with a speed of \(90 \mathrm{~km} / \mathrm{h}\).

Short Answer

Expert verified
The baseball has greater momentum than the bullet.

Step by step solution

01

Title - Convert Units

Convert the mass and velocity of the bullet and the baseball to consistent units (kilograms and meters per second). Mass of bullet: \(\text{4 g} = 0.004 \text{ kg}\) Velocity of bullet: \(\text{400 m/s}\)Mass of baseball: \(\text{150 g} = 0.15 \text{ kg}\)Velocity of baseball: \(\text{90 km/h = 25 m/s}\) (using the conversion \(1 km/h = 0.278 m/s\)).
02

Title - Calculate Momentum of Bullet

Use the formula for momentum, which is \( p = mv \), to calculate the momentum of the bullet.\( p_{\text{bullet}} = 0.004 \text{ kg} \times 400 \text{ m/s} = 1.6 \text{ kg m/s}\)
03

Title - Calculate Momentum of Baseball

Use the same formula for momentum to calculate the momentum of the baseball.\( p_{\text{baseball}} = 0.15 \text{ kg} \times 25 \text{ m/s} = 3.75 \text{ kg m/s}\)
04

Title - Compare the Momenta

Compare the calculated momenta to determine which is greater.\( 3.75 \text{ kg m/s} > 1.6 \text{ kg m/s} \)Thus, the momentum of the baseball is greater than that of the bullet.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

momentum formula
Momentum is a foundational concept in physics, used to describe the motion of objects. The momentum formula is given by: \[ p = mv \]where \( p \) is momentum, \( m \) is mass, and \( v \) is velocity. Momentum combines both the mass and velocity of an object. This means that even if an object is light, it can have a large momentum if it's moving quickly. Conversely, a heavy object moving slowly can also have substantial momentum.
Understanding this formula is crucial for solving physics problems related to movement and collisions. Remember, momentum has both magnitude and direction since it is a vector quantity.
unit conversion
Unit conversion is essential when solving physics problems, as consistency in units is key for accurate calculations. For example, in the provided exercise, units for mass and velocity must be converted to keep them consistent:
  • Mass: Convert grams to kilograms by dividing by 1000. For instance, 4g becomes 0.004kg.
  • Velocity: Convert km/h to m/s using the conversion factor \(1 \text{ km/h} = 0.278 \text{ m/s}\). So, 90 km/h converts to 25 m/s.
By converting all units to standard SI units (kilograms for mass and meters per second for velocity), we ensure that our calculations for momentum are correct and comparable.
comparison of momenta
After calculating the momentum of two objects, we often need to compare them. In our example, we calculated the momenta of a bullet and a baseball:
  • Bullet momentum: \( p_{\text{bullet}} = 0.004 \text{ kg} \times 400 \text{ m/s} = 1.6 \text{ kg m/s} \)
  • Baseball momentum: \( p_{\text{baseball}} = 0.15 \text{ kg} \times 25 \text{ m/s} = 3.75 \text{ kg m/s} \)
To compare them, we note that 3.75 kg路m/s (baseball) is greater than 1.6 kg路m/s (bullet). Thus, the baseball has greater momentum despite having a lower velocity because its mass is much larger.
physics problem-solving
Effective physics problem-solving requires a structured approach.
Here鈥檚 a step-by-step strategy:
  • Identify the given data and required unknowns.
  • Convert all units to be consistent (e.g., kg for mass, m/s for velocity).
  • Apply relevant formulas. For momentum, use \( p = mv \).
  • Calculate each required value step by step.
  • Compare the results to draw conclusions.
Using this method ensures that you thoroughly understand each part of the problem, leading to more accurate and confident solutions.

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