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Gauge pressure is the difference between the absolute pressure inside a system and the atmospheric pressure outside. In essence, it measures how much a system's pressure is above or below the surrounding environment's. This distinction is important because many environments, such as underwater ecosystems where jellyfish reside, are not at sea level air pressure.

In the jellyfish exercise, the gauge pressure is an impressive 15 MPa. This pressure is the force exerted over each square meter by the stinger's propulsion system. Scientists and engineers often use gauge pressure because it helps in calculating differences without needing to consider outside conditions. This makes problem-solving more straightforward in controlled environments.

• Gauge pressure = Absolute pressure - Atmospheric pressure
• Used primarily to calculate differences in controlled environments

Newton's Second Law is a fundamental principle in physics that describes the relationship between force, mass, and acceleration. It states that the acceleration of an object depends on two factors: the net force acting upon the object and the object's mass. The greater the force applied to an object, the more it will accelerate.

This law is expressed mathematically as \( F = m \cdot a \), where \( F \) stands for force, \( m \) for mass, and \( a \) for acceleration. This simple yet profound equation allows us to predict how an object will move when subjected to forces.

• Force is directly proportional to acceleration
• Force is inversely proportional to mass

Calculating force involves understanding the relationship between pressure and area. The problem gives us a pressure of 15 MPa, which needs to be converted into a force acting on the jellyfish stinger. To find this force, we use the formula \( F = P \cdot A \), where \( F \) is force, \( P \) is pressure, and \( A \) is the area.

To proceed, the area of the stylet must first be found. Given the diameter of 2.0 \( \mu \)m, the radius is half the diameter. This radius is used in the formula for the area of a circle: \( A = \pi \cdot r^2 \). After calculating the area, you can plug it into the force formula along with the pressure to find the force exerted on the stylet.

• Convert diameter to radius to find area
• Use \( A = \pi \cdot r^2 \)

Acceleration can be determined using Newton's Second Law once the force is known. In this exercise, we calculate how quickly the jellyfish's stylet accelerates due to the force of pressure. The second part of Newton's formula \( F = m \cdot a \) can be rearranged to find acceleration as \( a = F/m \). This rearranged equation tells us that acceleration is the result of dividing the force by the mass.

The given mass of the jellyfish stinger is an extremely light \( 1.0 \times 10^{-12} \) kg. Substituting this mass and the previously calculated force into the formula gives us the acceleration.

• Acceleration is force divided by mass
• Use rearranged formula \( a = F/m \)