exam02_sol_f10 - MASSACHUSETTS INSTITUTE OF TECHNOLOGY...

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MASSACHUSETTS INSTITUTE OF TECHNOLOGY Physics Department 8.01 Physics I Fall Term 2010 Exam 2 Solutions Name Section Table and Group With the exception of Problem 1, answers 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 free body diagrams when appropriate. Problem 1 (20 points) Problem 2 (25 points) Problem 3 (30 points) Problem 4 (25 points) Total (100 points) 1
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Problem 1a (5 points) Consider a rocket with speed v and maximum relative exhaust speed u . What is always true about the motion of the rocket in free space (that is, no gravity)? 1. It can not go faster than u (at which point the exhaust would be moving forward in the rest frame). 2. One needs another rocket stage to get v > u . 3. The mass of the remaining fuel is 0 when v = u . 4. More than one of the above. 5. None of the above. Answer 5 We found in class that starting from rest v = u ln[ m (0) /m ( t )]. We emphasized in class that if the rocket burns enough of its initial weight as fuel, the value of the logarithm can be greater than one and the rocket’s speed can exceed u .log 2
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Problem 1b (5 points) X56 X65 X78 A satellite (with mass negligible compared to that of the Earth) is making a fly-by of the Earth. Let the velocity of the Earth be ~v e = v e ˆ x . The satellite’s orbit is symmetric about a line through the center of the Earth and parallel to ˆ x . Far from the Earth the magnitude of the satellite’s x -component of velocity is v i when approaching and v f when receding. [You do not need angular momentum to do this problem.] For the case where v i = 3 v e , enter the numbers of any of the correct statements on the answer line below. 1. v f > v i . 2. v f = v i . 3. v f < v i . 4. v f > v e . 5. v f = v e . 6. v f < v e . Answer 3, 5 In a frame moving with the Earth, the satellite is approaching with an x component of velocity of v i - v e = 2 v e . There is no energy lost in the encounter, so in that frame it appears that the satellite has an elastic collision with an extremely massive object. Under those circumstances it bounces back with exactly the same magnitude of x velocity, 2 v e . Viewed from the rest frame, that v x is reduced by the speed of the Earth. Thus the satellite recedes from the encounter with v f = v e . 3
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Problem 1c (5 points) Cart B has twice the mass of Cart A. Each cart is initially at rest. You push cart A with twice the force that you push cart B, continuously from a starting line to a finish line. Let Δ p and Δ K be the change in a cart’s momentum and kinetic energy respectively. Which of the following statements is correct?
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