(hrw8c10p66) A uniform spherical shell of mass M = 2.5 kg and radius R = 20.0 cm

Question

(hrw8c10p66) A uniform spherical shell of mass M = 2.5 kg and radius R = 20.0 cm rotates about a vertical axis on frictionless bearings (see the figure). A massless cord passes around the equator of the shell, over a pulley of rotational inertia I = 3.42×10-3 kg m2 and radius r = 6.0 cm, and its attached to a small object of mass m = 1.0 kg. There is no friction on the pulley's axle; the cord does not slip on the pulley. What is the speed of the object after it has fallen a distance h = 0.9 m from rest: Use work - energy considerations. (If the picture didn't show up,the same picture in other questions are on chegg)

Explanation / Answer

Apply conservation of energy to solve the problem

Ei = Ef

1/2 mv^2 + 1/2 I w^2 + 1/2 I w^2 + mgyi = 1/2 mv^2 + 1/3 ( 2/3 MR^2( v/R)^2 + 1/2 I ( v/R)^2 + mg yf

0=1/2 m + 1/3 M + 1/2 I/R^2) v^2 + mgvf = 0

v = sqrt - mgyf/(1/2 m+ 1/3 M + 1/2 I/R^2)

= sqrt - ( 1.0 kg) ( 9.8) ( -0.9)/( 1/2(1) + 1/3(2.5) + 1/2 ( 3.42×10-3 kg m2/( 0.060)^2

=2.2 m/s

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