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A helicopter flies over the arctic ice pack at a constant altitude, towing an airborne 129-kg laser sensor that measures the thickness of the ice (see the drawing). The helicopter and the sensor both move only in the horizontal direction and have a horizontal acceleration of magnitude 2.84 $\mathrm{m} / \mathrm{s}^{2}$ . Ignoring air resistance, find the tension in the cable towing the sensor.

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1320 $\mathrm{N}$

Physics 101 Mechanics

Chapter 4

Forces and Newton’s Laws of Motion

Newton's Laws of Motion

Applying Newton's Laws

Cornell University

Simon Fraser University

Hope College

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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the doctor mind attention in the cable, we can use Newton's second law, So the tension in the cable has two components. One component is this one, the vertical component which counterbalances the weight. So let me call this T Y on the horizontal component, which is these one, and this is responsible for accelerating the laser sensor. So we will apply Newton's second law on in that direction. Let me choose my reference frame as this everything that is pointing to the right. It's positive and everything that is pointing it up. It's positive. Then, applying Newton's second law on the X direction results in the following the net force in that direction. Is it close to the mask off the sensor times its acceleration on that direction? There is only one force acting on the sensor in that direction, and these is the X component off the tension force, and this is equal to the mass off the sensor. 129 kilograms times its acceleration off 2.84 meters per second squared. This gives an X component off tension there is equals to 366.36 neutrons now applying Newton's second law on the vertical direction we get the following the net force in the vertical direction is it goes to the mass kinds next generation in that direction. But it's not accelerating in the vertical direction, so it's acceleration is close to zero than the Net Force in that direction. Is that close to zero truth? But there are two forces acting on the vertical axis, the white component off the tension force minus the weight force and this your vehicles to zero. So the white component off the tension force is equal to the weight force, which is given by the mass off the sensor times acceleration of gravity, which is approximately 9.8 meters per second squared there for the white component off the tension is Nico Studio 129 times 9.8, and these results, you know, 1264.2 Newton's now using this information. Now that we have both the acts on the Y components of detention, we can better mind what is the magnitude of pretension force? Because detention force forms that rectangle triangle like this. Here we have the Y component off the tension force. Here we have the X component off the tension force and here we have something that has the same magnitude as the full tension force. These is a 90 degree angle. Therefore, using the border if you're him. The full tension force has a magnitude. There is equal to the square root off the X squared plus two y squared. Then the magnitude of detention forces. It goes to the square it off. 366.36 squared plus 1264 with truth squared on. This results in attention force off approximately 1320 beautiful.

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