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Physics 325 Homework 3 - mass m and has a constant burn...

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Physics 325, Fall 2010 Prof. Susan Lamb Homework Assignment #3 Due Thursday 16 September at 11:15 am 1) (15 points) A rocket-propelled racing car has a total mass of m 0 and empty mass (after all of its fuel is burned) of m 1 . It attempts to set a land speed record. The car’s exhaust speed is u and it has a constant burn rate of α = - dm/dt . Ignore the friction of the wheels on the road and also ignore air resistance. The driver fires the rockets to accelerate the car from rest. After some time, he reverses the engines to decelerate the car back to zero speed (the rocket engines are always firing either forward or backward). a) What is the mass of the car (including remaining fuel) at which the driver should reverse the engines in order to maximize the car’s top speed? (Hint: all the rocket fuel should be burned at the end). b) What is the speed of the car as a function of time? 2) (15 points) A single-stage rocket is taking off from the surface of the Earth with initial
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Unformatted text preview: mass m and has a constant burn rate α and a relative exhaust velocity of U . At burnout, the mass of the rocket is m f . Assume that the gravitational acceleration is constant, and ignore air resistance. a) Determine the height of the rocket at burnout. b) Determine the maximum height of the rocket. 3) (15 points) A particle of mass m moves in the xy plane so that its position vector is an ellipse ~ r ( t ) = a ˆ x cos ωt + b ˆ y sin ωt a) Show that the net force on the particle points towards the origin. b) Compute the angular momentum of the particle about the origin (0 , , 0) as a function of time. c) Compute the angular momentum of the particle about the point ( a, , 0) as a function of time. d) Compute the torque ~ τ about the point ( a, , 0) as a function of time, and compare against the time rate of change of the angular momentum of the particle found in part c). 45 points total...
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