A 900-kg car is walking 20 m/s follow me a level road. How huge a constant retarding (friction) pressure is required to stop it in ~ a distance of 30m? (hint: discover the an unfavorable acceleration).

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This question talks about an elevator which is a mass of 4850 kg needs to be design so that the best acceleration is 0.068 G. Yet these are absolutely the acceleration because of the crab or the maximum and minimum forces the modem have to exert top top the supporting cable. For this reason we're going to do two situations over here. This is the an initial case where where this is the elevator, that's do it again. For this reason this is a forced elevator, This is the tension and also this is the weight. Currently in instance one, this is going up with the acceleration the a. And this is in the next case it is walk down through an acceleration that it. Let's talk about the case one. Therefore in the case one uh if you're gonna do the equation the the motion, that's walk to be t minus W is equal to massive of the acceleration. Most of the elevator times the acceleration. Uh therefore the stress is gonna it is in which we have to uncover is walk to it is in W plus M A. Now for the tension to it is in maximum, because that the attention to be maximum. Uh why we room taking this as a maximum, Let's allow me write the let me compose the equation for the 2nd case as well, it will make much more sense. In this case, w minus t is going come be equal to M. E. Due to the fact that the acceleration is pointing downwards. So if you're gonna rewrite T and t is going to it is in w minus mm. So we can clearly see the in in these 2 equations, this is going to result in a higher value the peace and also this is W plus and me and this is walking to an outcome in a lower value the peace and also this is W minus. So from this we room going to obtain the maximum value of T. And from this we are going to get the minimum worth of people. Currently the allude is as soon as will this it is in maximum? so this will certainly be maximum when c W is a constant mas is a constant, acceleration is the only thing which we can change. Therefore this is walking to be maximum as soon as acceleration is going to it is in maximum and the preferably acceleration is currently given end here. For this reason let's uh let's put the value of uh let's replace the blue through MG. And also this is uh this is M. A. Where is the best acceleration? so um is bring away out. We room left with G plus a max. Now let's instead of the worth of M. To be here, Moss is walk to be 4850. Therefore this is 4850. G is walking to be 9.8 plus. The best acceleration that 0.680 point 068 G. Okay, If the is in terms of G. And let's store this as G. Together well. Uh therefore let me grab mine calculator here and this is gonna be very same as one point let me just uncover at 1.68 times G. Times 4850. So it's going to be same to 50 76 2.04. Therefore this is the maximum stress and anxiety which the cable have the right to support. And definitely the unit has actually an newton's, an in similar way the exact same thing the you are going to perform over below as well. For this reason the only thing and also this finish equation is the authorize is minus. Therefore this is gonna it is in M g minus M a minimum. For this reason this is walk to be m times G minus a minimum. Again 0.0. Uh The maximum, yes this is no going to it is in minimum. So there is another thing mathematically i beg your pardon we need to understand over here. Uh This will certainly be minimum. This will be minimum Van. The just parameter i m sorry is transforming again is great. And mass is consistent acceleration is the just thing i m sorry is changing. For this reason if we need to make this minimum climate this component should it is in maximum. For this reason that we subtract the best thing and also we gain the minimum value. For this reason again acceleration is walking to it is in in the maximum end here. I m sorry is already given to us 0.068 G. Therefore we understand the worth of mass, that is 4850. And also g minus 0.068. GT method as the does permit me simply grab mine calculator and find us. So that's going come be equal to 1 -1068. Our time G. Times four, for this reason that's going to be equal to 44, 7 .96 and also the universe Newton. For this reason this is the minimum worth of the anxiety uh for the cable. So this are needs minimum and also the maximum worths uh the the stress or the forces the motor should exert top top the cable. Say thanks to you.