Problem 84 - College Physics

Question

BIO Momentum and the squirting squid. An interesting use of "rocket power" is that used by cephalopods such as octopi and squids. These animals take in seawater and then squirt it out at high speed. \(\mathrm{A} 2.5\) -kg squid can expel 0.25 \(\mathrm{kg}\) of seawater \((\mathrm{in}\) a short burst of 0.20 \(\mathrm{s} )\) with a speed of 600 \(\mathrm{cm} / \mathrm{s}\) What is the momentum of one squirt of water? $$\begin{array}{l}{\text { A. } 1.2 \mathrm{kg} \cdot \mathrm{m} / \mathrm{s} \text { in the direction of the squirt }} \\ {\text { B. } 1.5 \mathrm{kg} \cdot \mathrm{m} / \mathrm{s} \text { in the direction of the squirt }} \\\ {\text { C. } 12 \mathrm{kg} \cdot \mathrm{m} / \mathrm{s} \text { in the direction of the squirt }} \\ {\text { D. } 15 \mathrm{kg} \cdot \mathrm{m} / \mathrm{s} \text { in the direction of the squirt }}\end{array} $$

Step-by-Step Solution

Answer

Option B: 1.5 kg·m/s in the direction of the squirt.

Step 1: Understanding Momentum Formula

Momentum is calculated using the formula \( p = mv \), where \( p \) is momentum, \( m \) is the mass (in kg), and \( v \) is the velocity (in m/s).

Step 2: Converting Units

The speed given is 600 cm/s, which needs to be converted to meters per second because the standard unit for velocity in physics is meters per second (m/s). Since 1 meter is 100 centimeters, the speed is \( 600 \text{ cm/s} = 6 \text{ m/s} \).

Step 3: Calculating Momentum

Now, use the mass of the expelled water, which is 0.25 kg, and the converted speed of 6 m/s in the momentum formula: \( p = 0.25 \text{ kg} \times 6 \text{ m/s} \).

Step 4: Computing the Product

Perform the multiplication: \( p = 0.25 \times 6 = 1.5 \text{ kg} \cdot \text{m/s} \).

Step 5: Choosing the Correct Answer

The calculated momentum value is 1.5 kg·m/s. Therefore, the correct answer is option B: 1.5 kg·m/s in the direction of the squirt.

Key Concepts

Physics and Momentum

In physics, momentum is a key concept that helps us understand the motion of objects. It is the product of an object's mass and velocity, described by the formula \( p = mv \), where \( p \) represents momentum, \( m \) is mass, and \( v \) is velocity. This formula implies that momentum depends on both how much matter is moving (mass) and how fast it is moving (velocity).

• Mass: The amount of matter in an object, often measured in kilograms (kg).
• Velocity: The speed and direction of an object's motion, measured in meters per second (m/s).
• Momentum: A vector quantity, meaning it has both magnitude and direction.

In problems involving momentum, it is crucial to remember that the direction of motion is just as important as the speed. This idea is beautifully displayed by cephalopods like squids when they propel themselves forward.

Cephalopods: Nature's Rocket-Powered Creatures

Cephalopods, such as squids and octopi, are fascinating creatures that have developed an efficient method of movement using jet propulsion. These animals take in water and forcefully eject it out, allowing them to move in the opposite direction. This process not only helps them escape predators quickly but also exemplifies a practical use of the conservation of momentum. The expelled water functions much like a rocket engine for the cephalopod. When the water is ejected at high speed, it creates a momentum that propels the squid or octopus in the opposite direction. It showcases how creatures in nature utilize basic physical principles to survive in their environments. Understanding this natural phenomenon can illuminate broader concepts of physics and biology, especially how animals adapt to their habitats.

Unit Conversion: From Centimeters to Meters

Unit conversion is an essential skill in problem-solving, especially in physics where standard units enable consistent and accurate calculations. In the given problem, the squid's water jet speed is provided in centimeters per second (cm/s), but the calculation of momentum requires this to be converted to meters per second (m/s).

• Conversion Factor: 1 meter = 100 centimeters.
• Conversion Process: To convert 600 cm/s to m/s, divide by 100, resulting in 6 m/s.

Standardizing units to the international system helps in understanding and solving physics problems universally. This practice ensures that all measurements are in the correct format for calculations, reducing errors and facilitating clearer communication of physical principles.

Problem-Solving Strategies

Effective problem-solving in physics requires a systematic approach, starting with understanding the problem and deciding which principles and formulas apply. Here's a simple method to follow:

• Identify Known and Unknown Information: Determine what information is given and what needs to be found. In this case, the mass of the water and its velocity were known, while the momentum was unknown.
• Choose the Correct Formula: Use relevant physics formulas, such as \( p = mv \) for momentum.
• Convert Units if Necessary: Ensure all values are in the correct units for the formula chosen - as seen in converting cm/s to m/s.
• Perform Calculations Carefully: Execute the arithmetic operations required by the formula.
• Check the Result: Compare your answer with potential solutions or use logical reasoning to verify accuracy.

Adopting a structured approach not only assists in solving individual problems effectively but also bolsters general physics understanding and competence.