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## Challenge Homework 4 Physics 201

Challenge Homework 4Physics 201Due 11/13/20151. Box 1 sits atop box 2, which is attached via a masslessand frictionless pulley, and a very light rope, to box 3(see the diagram). The friction between the table andbox 2 is negligible but between box 1 and 2 the coefficient of static friction is 0.4 and the coefficient of kinetic friction is half that of static friction. The mass of box1 and 2 are both 2 kg. The mass of box 3 is as large as itcan be for box 1 to not slip relative to box 2 when thewhole system is released from rest. (a) Draw a freebody diagram for each box separately and identify allof Newtonâs 3rd law force pairs for after the system is released from rest. (b) What is the massof box 3? (c) If you were to now (after the system is released from rest) just barely tap on box 1in the opposite direction of motion, to break the static friction, box 1 would start to slide relative to box 2. If box 2 is a meter in length, how much time would it take for box 1 to slide offof box 2? Assume the table is very long and box 3 can fall for a very long distance.2. Two equal masses are connected by a light string via a massless,frictionless set of pulleys, as shown in the figure. (a) What is theacceleration of m1? (b) If both start from rest, how far has m2traveled after 3 s? Assume all surfaces are frictionless.3. The bottom 1-kg-mass in the figure, has the ability to make avariable incline of angle θ, for the top equally massive object toreside on. The bottom mass is on a frictionless surface, while thecoefficient of static friction between the two masses is 2/3. Aforce F, can be applied in the horizontal direction, as shown in the figure, on the bottom mass.(a) If the force F, is zero, what is the maximum angle the incline can be without the top massslipping? (b) If the angle θ is reduced to zero, what is the max force F, that can be applied tothe bottom mass without the top mass slipping? (c) The incline is now set to an angle of16.845Âº, what is the maximum force F that can be applied to the bottom mass and still not havethe top mass slip?4. A block (4.00-kg) is at rest on the right edge of alarge 11.0-kg slab. There is no friction below theslab and the horizontal surface it is on but there isfriction between the block and the slab. The coefficient of kinetic friction between the two is 0.25. The slab is 3.00 meters wide and a constanthorizontal force is applied to the left on the block. If it takes 2.00 s for the block to reach theother side of the slab, (a) what is the magnitude of the force applied to the block? (b) How fardoes the bottom block travel? (c) What is the final velocity of the top and bottom block? (Hint:use a non-moving/accelerating reference frame, i.e. static origin on the right side of the table)5. A Boeing 747 is fling in a horizontal circle that has a radius of9,300 m. If the planeâs wings make an angle of 30 degrees withrespect to the horizontal, what is the speed the plane must fly at tomake this turn and maintain its altitude?6. A mass of 3.0 kg is tied via a light string to the center of a table.A second mass of 5.0 kg is tied, also via a light string, to the firstmass. Both masses are made to undergo uniform circular motionat a rate of 10 revolutions per second. If the first mass is 1.2 mfrom the center of the table and the second mass is 2.0 m fromthe center of the table, what is the tension in both strings?7. A 1.0 kg weight, hanging vertically from the bottom of an inverted cone, is held in place by a2.0-kg-wheel that is rolling (without slipping) with a constant speed in a horizontal circle on theinside of the cone, as shown in the figure. They are attached by a string that passes through apulley and a hole in the middle of the cone. If the cone makes an angle of 20 degrees with respect to the horizontal and the wheel is always 1.0 m from the center line of the cone, what isthe a) maximum and b) minimum speed with which the wheel can go to keep the hangingweight in place, given the coefficient of static friction between the cone and the wheel is 0.4.

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