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Problem 74 Medium Difficulty

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.


1320 $\mathrm{N}$


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Video Transcript

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.