A An amusement park builds a ride in which the victim is mad

A) 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 170 kg. Neglect the mass of the rod of length 6 m .What is the moment of inertia of rider, box and rocket about the pole? The acceleration of gravity is 9.8 m/s^2 . Treat the rider, box and rocket as a point mass. Answer in units of kg · m^2

B) The rocket develops a thrust of 98 N perpendicular to the path of the rider. What is the initial angular acceleration of the rider? Answer in units of rad/s^2

C)After what time t is the rider’s velocity equal to 5 m/s? Neglect the change in mass of the rocket. Answer in units of s.

D)Gas exits the rocket at vt = 390 m/s. What mass per second must leave to develop the thrust F given above? Answer in units of kg/s .

Solution

I = M l² = 170 * 6²

I = 6120 kg.m²

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torque = l F = I alpha

alpha = l F / I = 6 * 98 / 6120

alpha = 0.096 rad/s²

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w = alpha t

v = l w = l * alpha t

t = v / l alpha = 5 / (6 * 0.096)

t = 8.68 s

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dm / dt = 98 / 390

= 0.251 kg/s