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# exam02_sol_f09 - MASSACHUSETTS INSTITUTE OF TECHNOLOGY...

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MASSACHUSETTS INSTITUTE OF TECHNOLOGY Physics Department 8.01 Physics I Fall Term 2009 Exam 2 Name Section Table and Group Answers on problems 2-5 without work shown will not be given any credit. Comments on how you are approaching the problem and what you are doing at any given point will be helpful to the grader in awarding partial credit, as will carefully drawn diagrams when appropriate. Problem 1 (20 points) Problem 2 (15 points) Problem 3 (20 points) Problem 4 (18 points) Problem 5 (27 points) Total (100 points) 1

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Problem 1a (5 points) A person is sliding on ice while holding a bag of sand that is slowing leaking sand from the bottom of the bag. There are no external horizontal forces acting on the person. In particular the ice is frictionless and one may ignore air resistance. While the sand is leaking, the speed of the person 1. increases, 2. decreases, 3. stays the same. 4. Not enough information is given to decide. Answer 3 There is no force exerted between the increment of sand separated from the bag and the person plus the remaining sand. Both maintain their horizontal velocities (and momenta) as the separation takes place. Eventually the separated sand hits the ground, but that has no influence on the continued motion of the person. 2
Problem 1b (5 points) Two objects A and B, starting from rest, are pushed with the same force for the same interval of time. Object B has twice the mass of object A. Circle the statements below that are true. 1. Both objects have the same change in momentum. 2. Object B has the greater change in momentum. 3. Object A has the greater change in momentum. 4. Both objects have the same change in kinetic energy. 5. Object B has the greater change in kinetic energy. 6. Object A has the greater change in kinetic energy. 7. Both objects travel the same distance in that time. 8. Object B travels further in that time. 9. Object A travels further in that time. Solution The integral of force times dt changes the momentum of the object. Equal forces for equal lengths of time produce the same change in momentum. The kinetic energy is given by p 2 / 2 m . Thus for the same momentum, the lighter object has the greater kinetic energy. The velocity is given by p/m . Thus for the same momentum, the lighter object has the greater velocity and will travel further in a given amount of time. 3

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Problem 1c (5 points) X55X28X78X29 X78 X41 X42 X43 X44 X45 X46 X47 The figure above shows a graph of potential energy U ( x ) verses position x for a particle executing one dimensional motion along the x axis. The total mechanical energy of the system is indicated by the dashed line. At t = 0 the particle is somewhere between points A and G. For later times, answer the following questions. 1. A At which point will the magnitude of the force be a maximum?
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