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This is the final exam for physics 7a- spring 2006 taught by lanzara. It covers topics such as work, energy, friction, angular motion, springs, and fluid mechanics. The exam consists of 5 problems and is closed book with a double-sided page of handwritten notes allowed. Calculators are permitted, but wireless ones are not. The exam is worth 105 points and partial credit is given for correct reasoning and work shown.
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This exam is closed book, but you are allowed a 8.5" x 11" (double-sided) page (double side) of handwritten notes. You may use a calculator, however NO wireless calculators are allowed. Anyone using a wireless calculator will forfeit their exam and automatically receive the score of zero. Don’t forget: a) Write your name, Discussion Section #, GSI name and SID# on the top of all materials you intend to hand in and want to be graded. b) Remember to circle all of your final answers and to clearly explain each step of your thinking. c) Express all numerical results to 3 significant figures. Cross out any work you decide is incorrect, with an explanation in the margin.
Read through the entire exam to start. Work to maximize your credit – a) Start with the problems you are more familiar with. B) Try to obtain at least partial credit on every part of every problem.
You push a box of mass m, which is initially at rest on a horizontal table, by a distance x, with a horizontal force F. The coefficient of kinetic friction between the box and table is μ. a) (5pts) Find the external work done on the bock-table system b) (2pts) Find the energy dissipated by friction c) (3pts) Find the speed of the box
A string is wrapped several times around the rim of a small hoop with radius 0.0800m and mass 0.180kg. If the free end of the string is held in place and the hoop is released from rest, calculate: a) (5pts) The tension in the string while the hoop descends as the string unwinds. b) (4pts) The time it takes the hoop to descend y=0.750m c) (5pts) The angular speed of the rotating hoop after it has descended y=0.750m. Assume now that the string is wrapped to a yo-yo that is initially at rest on a horizontal surface. We now pull the string in three different ways (see panel b). d) (3pts) Draw the free-body diagram for each case. e) (3pts) In what direction will each rim rotate? Explain your answer.
An homogeneous disc of radius R= 20cm, mass M= 2.0 kg and momentum of inertia MR^2 /2 lies on a table and can rotate on an horizontal plane (no friction) around a vertical axis through the origin O (see figure) with initial angular velocity ω 0 = 5.0s-1. A particle of mass m= 0.10 kg can freely move without friction along a straight guide on the disc, that goes from the origin of the disc to the external point. Neglect the contribution of the guide to the total momentum of inertia of the disc.
c) (2pts) Derive an expression for the tension in the cord when the elevator is accelerating downward with an acceleration of magnitude a = 1/3 g downward. d) (3pts) What is the tension when the elevator is in free fall with a downward acceleration equal to g? e) (10pts) Find the time it takes the beaker to empty as a function of h. Neglect the volume of the block.