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Physics 325 Spring 2011 Problem Session 4

# Physics 325 Spring 2011 Problem Session 4 - up What is m 1...

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Physics 325 Spring 2011 Discussion 4 February 14, 2011 Problem 1 Suppose a rocket can eject fuel to the back (to accelerate) or to the front (to decelerate) at a constant rate dm/dt = - α . Assume there is no other force, so the equation of motion is m dv dt = uα, where u = u 0 when it is accelerating, and u = - u 0 when it is decelerating. The initial mass of the rocket is m i , and its mass when it is out of fuel is m f . Starting from rest, the rocket accelerates until its mass is m 1 . Afterwards, it decelerates until all of its fuel is used
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Unformatted text preview: up. What is m 1 expressed in terms of m i and m f if the rocket stops moving when all of the fuel is gone? Problem 2 A force ﬁeld has the form (in cylindrical coordinates): ~ F =-k r ˆ φ, where k is a constant. (a) Calculate H ~ F · d ~ ‘ around a unit circle centered at the origin. (b) Based on the previous result, is the force ﬁeld conservative ? Why or why not? (c) Let W = k arctan ± y x ² . Calculate-~ ∇ W ....
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