An amusement park builds a ride in which the victim is made to spin about a pole

Question

An amusement park builds a ride in which the victim is made to spin about a pole with a rocket strapped on his seat. The rider, box and rocket have an initial total mass of 150 kg. Neglect the mass of the rod of length 7 m. A) What is the moment of inertia of rider, box and rocket about the pole? The acceleration of gravity is 9.8 m/s2 . Treat the rider, box and rocket as a point mass. B) The rocket develops a thrust of 60 N perpendicular to the path of the rider. What is the initial angular acceleration of the rider? C) After what time t is the rider

Explanation / Answer

(a) > I found this to be I=MR^2, which was 5500kg/m^2 I agree. (I'm assuming "the rod" extends perpendicularly to "the pole" and the rider is attached to it. This wasn't too clear in the question.) (b) Angular acceleration = (linear acceleration) / R "R" is 5 meters; and you can figure out the linear acceleration using F=ma (they give you "F" and "m") However, I'm confused by the phrase, "...a thrust of 83N perpendicular to the path of the rider." Perpendicular to the path??? I assume this is an error, and they mean "perpendicular to the radius" or something. Otherwise, I can't picture the scenario. (c) Use F=ma again, only write it as: "F=m(?v/t)". They give you F, m and ?v; solve for "t". (d) Force equals the rate of change of momentum. Say the rocket kicks out ?m of fuel every "t" seconds. It does this by exerting a force on the fuel, accelerating it from zero to speed v_i. So, the rocket is changing the fuel's momentum at a rate of: (?m)(v_i) / t. This is the force that the rocket exerts on the fuel; and therefore is the force that the fuel exerts on the rocket: F = (?m)(v_i) / t The number you want is ?m/t, the rate of fuel expulsion: ?m/t = F/(v_i) They give you F (83N) and v_i; now divide.

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