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A jet flying at 123 m/s banks to make a horizontal circular turn. The radius of the turn is 3810 m, and the mass of the jet is $2.00 \times 10^{5} \mathrm{kg}$. Calculate the magnitude of the necessary lifting force.

$2.12 \times 10^{6} \mathrm{N}$

Physics 101 Mechanics

Chapter 5

Dynamics of Uniform Circular Motion

Newton's Laws of Motion

Applying Newton's Laws

Cornell University

University of Washington

Simon Fraser University

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.

03:43

In physics, dynamics is the branch of physics concerned with the study of forces and their effect on matter, commonly in the context of motion. In everyday usage, "dynamics" usually refers to a set of laws that describe the motion of bodies under the action of a system of forces. The motion of a body is described by its position and its velocity as the time value varies. The science of dynamics can be subdivided into, Dynamics of a rigid body, which deals with the motion of a rigid body in the frame of reference where it is considered to be a rigid body. Dynamics of a continuum, which deals with the motion of a continuous system, in the frame of reference where the system is considered to be a continuum.

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in this problem. We have a plane flying on a bank curve and we have to find the magnitude of the lifting force for the force under a plane's wings that keeps airborne that we need in order. Tow fly at this radius and velocity. So if you draw free body diagram er of our plane, we have the gravitational force pointing downward and the normal force pointing perpendicular to our banked curve like this. Now, in a more detailed diagram, we can see that our normal force must be equal to the song of Ah, why component and an ex component with the angles data between them here. Now we can see that. And that, um, are why component must be counter acting the force of gravity. Is this pointing straight upward and buy some more detailed diagram where we sort of the forces because he had This must also be equal to FN times the co sign with data or sorry, not and in this case, f l r lifting for. Since we're not on the ground now, X component is pointing straight inward towards the center of our circular motion, so it must be equal to the centripetal force fan base in the trigonometry of our problem. It is also equal to science data with our problems. Now we can solve for the lifting force itself in terms of mg based on our white component must be mg divided by Costa. And that means that we can rewrite ah horizontal component as well as mg 10 of data. Since the tangent is just equal to sign if they've divided by co sign of data, as we said earlier, that is equal to the centripetal force M V squared over our now we can cancel out our ends. And even though f l isn't in our problem anymore, as we know for earlier, f l is equal to mg over coast data. So we're going to solve the equations that we have now for theta in order to solve. The problem is a hole, so let's rearrange toe isolate 10 if data and get that 10. If data equals b squared over our times G and when we plug in the numbers that were given, which is that we're traveling but 123 meters per second squared and a radius is 3810 meters multiplied by 9.8 meters per second squared. We've, um, kind of the inverted. We find that data is equal to 22.0 for eight degrees using the inverse tangent function. So 10 negative one. This data, all that's left to do now is to plug in. We know from earlier that f l equals mg overcoats. If data were given the mass of the plane as two times 10 to the fifth kilograms comes 9.8 meters per second. Divided by co sign of that angle that we just found and political dissent Tour calculator. We find that it is equal to 2.115 times 10 power of six. Our units are meters times are excuse me kilograms times meters per second squared which is equal to Newton's, the units of force So answer makes sense And this is our value for the lifting force

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