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Problem 76 Easy Difficulty

A rescue helicopter is lifting a man (weight 822 N) from a capsized boat by means of a cable and harness. (a) What is the tension in the cable when the man is given an initial upward acceleration of 1.10 $\mathrm{m} / \mathrm{s}^{2} ?$ (b) What is the tension during the remainder of the rescue when he is pulled upward at a constant velocity?


914 $\mathrm{N}$
822 $\mathrm{N}$


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Video Transcript

determined attention in the cable. In the situation, we can use Newton's second law specifically in the direction because there are only forces acting in this direction. Let me call. There's the Y direction and everything that is pointing up. We'll be positive in my reference frame and everything that is pointing now will be negative. As a consequence, then Newton's second law tells us the following the net force that acts on the man that is being rescued is he goes to the mass off that man times its acceleration. Then the net force we can see is given by the composition of two forces attention force that points to the positive direction minus the wait for switch points. The negative direction and these is equal to the mass off the man times acceleration. Therefore, detention is he goes to the mass off the men times its acceleration plus its weight. Then in the second item, the tension is given by the mass off the man which we don't have. What you have his weight, then remember, that's the weight is equal to the mass change. The acceleration of gravity near the surface off the earth, which is approximately 9.8 meters per second squared, so we can complete the mass as the weight divided by the acceleration of gravity. So for the mass, we have the weight divided by the acceleration of gravity times the acceleration, that situation plus the weight. But the weight off the guy is given in the problem. The weight is equals to 822 neutrons, so 822 divided by G times a plus the weight again, These results in attention force off approximately 914 you times for these item on the next item. Detention force is equals to the weight force because the acceleration is in close to zero. So these term vanishes from the equation for detention. So it's very close to 822 neutrons in the second item.