A large wooden turntable in the shape of a flat uniform disk has a radius of 1.65 m and a total mass of 135 kg. The turntable is initially rotating at 3.10 rad/s about a vertical axis through its center. Suddenly, a 65.5-kg parachutist makes a soft landing on the turntable at a point near the outer edge.
(a) Find the angular speed of the turntable after the parachutist lands. (Assume that you can treat the parachutist as a particle.) 1.04 Incorrect: Your answer is incorrect. rad/s
(b) Compute the kinetic energy of the system before and after the parachutist lands. KEbefore = 883.1 Correct: Your answer is correct. J
KEafter = 297.3 Incorrect: Your answer is incorrect. J
here,
mass of table , m1 = 135 kg
mass of Parachuist , m2 = 65.5 kg
initial speed , w0 = 3.1 rad/s
a)
let the final angular speed be w
using conservation of agular momentum
0.5 * m1 * r^2 * w0 = ( 0.5 * m1 * r^2 + m2 * r^2 ) * w
0.5 * 135 * 1.65^2 * 3.1 = ( 0.5 * 135 * 1.65^2 + 65.5 * 1.65^2) * w
solving for w
w = 1.57 rad/s
the final angular speed is 1.57 rad/s
b)
the initial kinetic energy , KE0 = 0.5 * I * w0^2
KEi = 0.5 * m1 * r^2 * w0^2
KEi = 0.5 * 0.5 * 135 * 1.65^2 * 3.1^2 J
KEi = 883.1 J
the final kinetic energy , KEf = 0.5 * (0.5 * m1 * r^2 + m2 * r^2 ) * w
KEf = 0.5 * ( 0.5 * 135 * 1.65^2 + 65.5 * 1.65^2) * 1.57 J
KEf = 284.2 J
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