(II) (a) What is the acceleration of two falling sky divers (mass 132 kg including parachute) wh

step 1 For part A, we want to find the acceleration of the skydivers. If we look at some of the forces,

(II) (a) What is the acceleration of two falling sky divers...

(II) $(a)$ What is the acceleration of two falling sky divers (mass 132 $\mathrm{kg}$ including parachute) when the upward force of air resistance is equal to one-fourth of their weight? $(b)$ After popping open the parachute, the divers descend leisurely to the ground at constant speed. What now is the force of air resistance on the sky divers and their parachute? See Fig. $4-39$ .

Key Concepts

Newton's Second Law of Motion

This principle states that the net force acting on an object is equal to the mass of the object multiplied by its acceleration (F = ma). It is fundamental in analyzing the motion of objects under various forces, including gravitational pull and air resistance, as it allows one to determine the resultant acceleration when forces are unbalanced.

Gravitational Force (Weight)

Gravitational force, commonly known as weight, is the force acting on a mass due to gravity. It is calculated by multiplying the mass of the object by the acceleration due to gravity. This concept is essential when comparing forces acting on an object, such as opposing air resistance, to understand the net force and resulting acceleration.

Air Resistance (Drag Force)

Air resistance is the force that opposes the motion of an object through air. In dynamics, it is crucial to include this force when analyzing the motion of objects falling under gravity. Depending on its magnitude relative to weight, air resistance can reduce the net force acting on the object, thereby decreasing its acceleration or even balancing the gravitational force under steady conditions.

Equilibrium Condition

Equilibrium in mechanics refers to a state where all the forces acting on an object balance each other, resulting in no net force and, consequently, no acceleration. When an object reaches this state, such as descending at a constant speed, the upward force (like air resistance) exactly equals the downward gravitational force, thereby creating a balanced system.

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