Suppose you go skydiving. a. Just as you fall out of the airplane, what is your gravitational acceleration? b. Would this acceleration be bigger, smaller, or the same if you were strapped to a flight instructor, and so had twice the mass? c. Just as you fall out of the airplane, what is the gravitational force on you? (Assume your mass is \(70 \mathrm{kg}\).) d. Would the gravitational force be bigger, smaller, or the same if you were strapped to a flight instructor, and so had twice the mass?

Newton's second law of motion is a fundamental principle that describes the relationship between an object's mass, the force acting upon it, and its acceleration. The law is typically expressed with the formula \( F = m \times a \). Here, \( F \) stands for force, \( m \) stands for mass, and \( a \) stands for acceleration. This law tells us that the force acting on an object is directly proportional to both its mass and the acceleration it undergoes. For example, if you are skydiving and have a mass of 70 kg, the force due to gravity (gravitational force) pulling you down is calculated by multiplying your mass by the acceleration due to gravity (\( g \)), which is approximately 9.8 m/s\textsuperscript{2}. This yields a gravitational force of 686 N (Newtons). When you understand this principle, it becomes clear how forces influence motion.

Gravitational force is the force that attracts every object with mass towards the center of the Earth. This force is crucial for understanding not only skydiving but many other phenomena on Earth and in space. The formula to calculate gravitational force is: \( F = m \times g \). Here, \( F \) is the gravitational force, \( m \) is the mass of the object, and \( g \) is the gravitational acceleration (roughly 9.8 m/s\textsuperscript{2} on Earth).

If you were skydiving with a mass of 70 kg, the gravitational force on you would be calculated like this: \( 70 \times 9.8 = 686 \mathrm{N} \). If you were to skydive with a flight instructor, doubling the mass to 140 kg, the gravitational force would double as well: \( 140 \times 9.8 = 1372 \mathrm{N} \). This shows that gravitational force is directly proportional to mass.

The relationship between mass and gravity is a vital concept in physics. Gravitational acceleration (\( g \)) remains constant near the Earth's surface, regardless of the mass of the object. This principle can sometimes be counterintuitive because we might think that heavier objects fall faster. They don’t.

In reality, the gravitational acceleration is the same for any object, whether it's a single person or a person strapped to a flight instructor. So, if you and your instructor were together, you'd fall with the same acceleration of 9.8 m/s\textsuperscript{2}. However, because the combined mass is greater, the total gravitational force would be greater, although the rate at which you fall remains unchanged.

This insight is crucial for understanding why skydivers, regardless of their individual masses, can fall at the same rate when they jump from an airplane.