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A $7650-\mathrm{kg}$ helicopter accelerates upward at 0.80 $\mathrm{m} / \mathrm{s}^{2}$ whilelifting a 1250 -kg frame at a construction site, Fig. $59 .$(a) What is the lift forceexerted by the air onthe helicopter rotors?(b) What is the tension inthe cable (ignore its mass)that connects the frame tothe helicopter? (c) Whatforce does the cable exerton the helicopter?

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a. $9.43 \times 10^{4} \mathrm{N}$b. $1.33 \times 10^{4} \mathrm{N}$c. $1.33 \times 10^{4} \mathrm{N}$

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

University of Michigan - Ann Arbor

Simon Fraser University

Hope College

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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So here we have the free body diagram for the helicopter and the frame with with which it is carrying. So we can say that the sum of forces in this case would be in the UAE direction. There isn't any force in the extraction and this is going to be equal to the force of lift minus the mass of the helicopter, plus the mass of the frame times the acceleration due to gravity G. And this is equaling the mass of the helicopter, plus the mass of the frame times the system's acceleration. So we can say that the force of the lift would be equal to the mass of the helicopter, plus the mass of the frame multiplied by the acceleration of the system, plus the acceleration due to gravity. And at this point, we can solve. So the force of the lift well, then the equal to 7650 kilograms before the mass of the helicopter plus 1250 kilograms, which would be the mass of the frame, multiplied by 9.8 plus 0.8 meters per second squared. And so we can say that the force of the lift is going to be equal to 9.43 times 10 to the fourth Nunes. This would be our answer for the force of the lift. Now this is the free body diagram for the frame. And so we can say that the sum of forces in the war direction would of course be forced tension minus the mass of the frame times G. And this is again equaling the mass of the frame times the acceleration of the system itself. Therefore, the force tension in the when the cables that is carrying the frame would be equal to the mass of the frame multiplied by the acceleration due to gravity, plus the acceleration of the system itself we can then solve. And this is equally 1250 kilograms. This would be the mass of the frame times 9.8 plus 0.8 a meters per second squared and we find that the force tension would be equal to 1.33 times 10 to the fourth Nunes. Now, this would be our answer for the force tension. Now, at this point, we can. For part C, it's going to be the exact same answer. So this is your answer for part B. However prepared to see is asking us for the ah force tension that acts downwards on the helicopter. And due to Newton's second law of Motion, every, um, uh, every force, right? Every force produces an equal and opposite reaction. Therefore, the forced tension would be equal to 1.33 times 10 to the fourth noons. And then let's specify direction downwards on the helicopter. That is the end of the solution. Thank you for watching.

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