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(II) $(a)$ What is the acceleration of two falling sky divers(mass $=132$ kg including parachute) when the upward forceof air resistance is equal to one-fourth of their weight? (b) After popping open the parachute, the divers descend leisurelyto the ground at constant speed. What now is the force of airresistance on the sky divers and their parachute? See Fig, $32 .$

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a. $-7.35 \mathrm{m} / \mathrm{s}^{2}$b. $1.29 \times 10^{3} \mathrm{N}$

Physics 101 Mechanics

Chapter 4

Dynamics: Newton's Laws of Motion

Motion Along a Straight Line

Motion in 2d or 3d

Newton's Laws of Motion

Applying Newton's Laws

Moment, Impulse, and Collisions

Rutgers, The State University of New Jersey

University of Sheffield

University of Winnipeg

Lectures

03:28

Newton's Laws of Motion are three physical laws that, laid the foundation for classical mechanics. They describe the relationship between a body and the forces acting upon it, and its motion in response to those forces. These three laws have been expressed in several ways, over nearly three centuries, and can be summarised as follows: In his 1687 "Philosophiæ Naturalis Principia Mathematica" ("Mathematical Principles of Natural Philosophy"), Isaac Newton set out three laws of motion. The first law defines the force F, the second law defines the mass m, and the third law defines the acceleration a. The first law states that if the net force acting upon a body is zero, its velocity will not change; the second law states that the acceleration of a body is proportional to the net force acting upon it, and the third law states that for every action there is an equal and opposite reaction.

04:30

In classical mechanics, impulse is the integral of a force, F, over the time interval, t, for which it acts. In the case of a constant force, the resulting change in momentum is equal to the force itself, and the impulse is the change in momentum divided by the time during which the force acts. Impulse applied to an object produces an equivalent force to that of the object's mass multiplied by its velocity. In an inertial reference frame, an object that has no net force on it will continue at a constant velocity forever. In classical mechanics, the change in an object's motion, due to a force applied, is called its acceleration. The SI unit of measure for impulse is the newton second.

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Graham. Ah, going up would be the force of air resistance. And then going down would of course be the mg the force of gravity. Eso weaken for party. We want to find the acceleration. So we know that the sum of forces is going to be equal to mass times acceleration and this would be equal to the force of air resistance minus mg. So we're choosing up to be positive and this would be equal point 25 mg minus mg and then this is equaling m A. So the masses cancel out, of course, and we find that a the acceleration will be equal to negative 0.75 times g. The fact that is negative, this means that it's going the acceleration is going to be directed downwards because we chose up to be positive. So this is gonna equal negative 0.75 times 9.8 meters per second squared and this is gonna equal negative 7.35 meters per second squared and again the direction here because of his negative, would be considered downwards. And then for part B, we want the force of air resistance such that we're moving. We're descending at a constant velocity. So if we're descending at a constant velocity, that means that there is no acceleration, Michael. No acceleration. Which means that the sum of forces will equal m A. However, this is gonna equal zero. And this vehicles of force of air resistance minus mg So essentially the force of air assistance would be equal to the weight ain't. And then you solve at this point. So 132 kilograms times 9.8 meters per second squared. And this is giving us 1.29 times 10 to the third unions. So this would be your answer for part B the force of the air resistance such that we're descending at a constant velocity and then for part A we ever just our acceleration pointed downwards. That is the end of the solution. Thank you for watching

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