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MIT 8 01T - Problem Solving: Momentum, Impulse, and Conservation of Momentum

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Problem Solving: Momentum, Impulse, and Conservation of Momentum 8.01 W05D3 Today’s Reading: Chapter 10 Momentum, System of Particles, and Conservation of Momentum Sections 10.9 Chapter 12 Momentum and the Flow of Mass Sections 12.2,12.3Announcements Problem Set 4 due Week 6 Tuesday at 9 pm in box outside 26-152 Sunday Tutoring in 26-152 from 1-5 pm Math Review Week 6 Tuesday 9-11 pm in 26-152.Table Problem: Rocket Sled A rocket sled can eject gas backwards or forwards at a speed u relative to the sled. The mass of the fuel in the sled is equal to dry mass of the sled, m0 . At t = 0 the rocket sled has speed v0 and starts to eject fuel in the forward direction in order to slow down. You may ignore air resistance. You may treat u as a given constant in the following questions. a) Derive a relation between the differential of the speed of the rocket sled, dvr , and the differential of the mass of the rocket sled, dmr. b) Integrate the above relation to find the speed of the rocket sled as a function of mass, vr(mr), as the rocket sled slows down. c) What was the initial speed v0 of the rocket sled if the sled came to rest just as all the fuel was burned?Table Problem: Car Driving Off Barge A workman is unloading the last car (mass mc ) from a barge (mass mb ) tied to the pier by a short cable. He drives with a constant acceleration from a standing start and attains a speed vf in the time tf it takes to reach the end of the barge. a) Does this put tension in the cable or does it push the barge against the dock? b) Depending on your answer to a) determine an expression for either the tension T(t) in the cable or the magnitude of the horizontal force F(t) of the pier on the barge during the time t = 0 to t = tf . Express your answer in terms of some or all of the quantities mc , tf, mb and vf as needed.Extra Group Problem: Acrobat and Clown An acrobat of mass mA jumps upwards off a trampoline with an initial y-component of velocity vy,0 = v0. At a height h0, the acrobat grabs a clown of mass mB. Assume the acrobat grabs the clown during a time interval that is negligibly small. a) What is the velocity of the acrobat immediately before grabbing the clown? b) What is the velocity of the acrobat immediately after grabbing the clown? c) How high do the acrobat and clown


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MIT 8 01T - Problem Solving: Momentum, Impulse, and Conservation of Momentum

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