Every course in mechanics comes with tedious problems where masses do silly things like slide on inclined planes, hang o

[answerhappygod]

Every Course In Mechanics Comes With Tedious Problems Where Masses Do Silly Things Like Slide On Inclined Planes Hang O 1 (184.36 KiB) Viewed 19 times

Here is the question. The picture is the set up.
Consider the Atwood machine in the sketch below (left). Find thetension T0 in the uppermost string and the acceleration a0 of theleftmost mass m. You should have found that T0 is not the same as(m + m0 )g. How can this be, given that the tension in the stringneeds to support the weight of both masses?
Every course in mechanics comes with tedious problems where masses do silly things like slide on inclined planes, hang on pulleys, and so on. I hate these problems with every fiber of my being, but I cannot ignore their importance. So I'll cut us a deal: you do this one ridiculous pulley/incline problem, and in return I will never return to such exercises again. Well, here we go. A large block of cheddar, initially of mass Mo, sits on a cheese grater inclined at an angle to the horizontal. The surface of the grater is rough, with coefficient of friction. The cheddar is attached to a pulley at the top of the ramp by a massless string. The pulley hangs over the top of the grater and is attached to the infinite sequence of pulleys and identical masses m, as shown below. M T m m ܗ܀ The system is released from rest, and the cheddar starts to slide downwards under the influence of gravity. As it slides, it rubs against the grater and leaves behind some shredded cheese. The mass left behind is proportional to the distance x the block has slid, so the mass of the cheddar is given by M = Mo(1-3x), where 3 is a constant. At some point, the block will lose enough mass that it cannot counterbalance the other forces, and it will stop. The goal of this problem is to figure out how far it slides, and how much cheese will be left over when it comes to rest. We'll proceed in stages: first we will analyze the infinite pulley system; then we will analyze the dynamics of the sliding cheese; and finally we will make a few approximations to extract useful information. You may find steps 1-15 of this