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Problem 107 Hard Difficulty

ssm mmh The drawing shows Robin Hood (mass 77.0 $\mathrm{kg}$) about to escape from a dangerous situation. With one hand, he is gripping the rope that holds up a chandelier (mass 195 $\mathrm{kg}$). When he cuts the rope where it is tied to the floor, the chandelier will fall, and he will be pulled up toward a balcony above. Ignore the friction between the rope and the beams over which it slides, and find (a) the acceleration with which Robin is pulled upward and (b) the tension in the rope while Robin escapes.

Answer

4.25 $\mathrm{m} / \mathrm{s}^{2}$ \
1080 $\mathrm{N}$

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Video Transcript

for this question and have to use Newton's second law for that. Let me choose the falling reference frame, a vertical axis pointing upwards that I'm calling white on the first item. We have to calculate what is Harding's acceleration for that to have to use Newton's second law. It tells us that applying on, robbing the net, force acting, robbing is it close to his mass times his acceleration, the net force acting or holding ISTEA the tension on the weight force. So we have t pointing to the post in direction, minus the weight force, pointing to the negative direction because to his mass times his acceleration. Now, if we applied on the chandelier, we get the following. So for the Shanda Lee, the Net force acting on it is even by its mass finds its acceleration. Note that the acceleration off the Shanda Lee we were the same as the acceleration off Harding because the hope is considered to be ideal. Then we have the tension force pointing upwards minus the weight off the shadow Lee, which points downwards, and these is equal to the mass off the chandelier times acceleration. But notice that the chandelier We'll go down. So it's acceleration is negative, for we have a minus. Sign here. Then we can use the equation for the chandelier to discover an equation for the tension and then seeps into detention to solve for acceleration off Having say it goes as follows, attention is given by the weight of the chandelier, minus the mass off the chandelier times acceleration. Now, substituting these equations, we get the following the weight off the chandelier minus and mass off the chandelier times the acceleration off the chandelier miners the weight off having his ecos to the mass times acceleration of harming, then sending this term to the other side. We get the way you see when there's nobody being equals. Two m times A plus M C. Times eight. Now we can fact for a on the right hand side to get a Times M plus M C. Then send this term to the other side. Dividing to get a is equal to the weight off the chandelier miners the weight off Robin Hood divided by the mass off Robin Hood, plus the mass off the chandelier. Remembering that the weight is given by the mass off the object times the acceleration of gravity. We get an acceleration for Harvey huge that is given by the weight off the chandelier. Say See times G minus the weight off. Having heard which m. Times G and it was divided by M plus m. C, we can further a factor g to get yet acceleration is the question. G times M C minus TEM, divided by m plus m c in the values that were given by the problem. Results in 9.8 times 195 minus 7 to 7, divided by 195 plus seven. Seven on these results in an acceleration off approximately 4.25 meters per second squared. So these is rubbings acceleration. Now for the next item, we have to calculate what is the tension? The hope for that We can use these equation now that you know the acceleration. So the tension is given by the weight off the chandelier, which is its mass times. Acceleration of gravity. Mine is the mass of the chandelier finds its acceleration. So the tension is given by the mass of the chandelier. Times G minus eight. Plug in the values we got the following t is equals to 195 times 9.8 miners for 2025 and this results in attention off approximately 1000 and 80 year terms. So this is the tension in the hope.

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