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Material Type: Assignment; Class: Mechanics; Subject: Physics; University: Lafayette College; Term: Spring 2009;
Typology: Assignments
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April 7, 2009
Physics 131 Level II Homework Set Section 1
You may discuss these problems with one or two other students (or with your instructor), but your final solutions should be written out by you alone. Under no circumstances should you see another student’s written solutions. If you have discussed these problems with anyone you must acknowledge the collaboration at the beginning of the corresponding problem. Homework is due in my office by 3:30 PM on the due date and solutions will then be made available on the course web site. No homework will be accepted after this time.
You are expected to carefully explain how, starting from basic principles, you have arrived at your answers. Please do not use paper with edges frayed from being ripped out of a spiral bound notebook. If the papers are illegible or disorganized, we reserve the right to return these papers without being graded. Unless instructed otherwise, all answers should be correct to 3 or 4 sig. figs.
Assignment 10: Due Monday, April 13, 2009
Problem 1: Consider a large square, length L on edge, suspended from a vertex (corner) and rotating in the vertical plane of the square with the axis of the rotation being horizontal. When the square is at equilibrium, the diagonal passing through the point of suspension is vertical and defines the θ = 0 position. The mass of the square is M and the gravitational field is g.
If the square is now lifted to some angle relative to the vertical and then released, it will oscillate back and forth in the vertical plane (ignore any frictional effects). Find the ex- pression for the angular acceleration as a function of θ. Does this kinematics fall into any one of the types that we have studied to date. Explain why or why not.
Assume the square is released from rest from an angle of 90 degree. What is the expres- sion for the angular speed when the square is in the vertical position θ = 0. Ignore any frictional effects.
Problem 2: Consider Figure 10-55 in the text. Let the length of each rod be L as in the text, but let each rod have a diameter of D with D = 0. 2 L , with L and unspecified number. If the sys- tem is released from rest with the H in a vertical position (straight up), what is the linear speed of the outer tip when it is again vertical but straight down?
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April 7, 2009 Page 2
Problem 3: Consider a hoop and a solid uniform disk, each with the same mass M and outer Radius R. They are started from the same point on an inclined plane which makes an angle of θ with the horizontal. They both roll down the incline a distance D to the bottom. Assume rolling without slipping for both.
Using energy conservation, find the translational speed (the speed of the center of mass) of each, and using that result, argue as to which gets to the bottom first.
Now do a Newton II analysis to find the linear acceleration of both systems and find the ratio of the times it takes each to get to the bottom. Is your result consistent with that in Part A?
Problem 4: A space ship has an accident while trying to dock at a space station. Model the space ship as a point particle and the space station as a ring with an outer radius of R and an in- ner radius of 0. 75 R. The space ship has a mass of M and is approaching the space station along a straight line that is tangent to the outer circumference of the space station. The space ship hits the docking station with a speed of V , smashing into the docking station and lodging in place. If the mass of the station is ten times the mass of the ship, what is the final angular velocity of the station if it was zero to start. Your answer should be a pure number times some expression in- volving M , V , and R.