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A uniform spherical shell of mass M ! 4.5 kg and radius R
Chapter , Problem 66(choose chapter or problem)
A uniform spherical shell of mass M = 4.5 kg and radius R = 8.5 cm can rotate about a vertical axis on frictionless bearings (Fig. 10-47). A massless cord passes around the equator of the shell, over a pulley of rotational inertia \(I=3.0 \times 10^{-3} \mathrm{~kg} \cdot \mathrm{m}^{2}\) and radius r = 5.0 cm, and is attached to a small object of mass m = 0.60 kg. There is no friction on the pulleys axle; the cord does not slip on the pulley. What is the speed of the object when it has fallen 82 cm after being released from rest? Use energy considerations.
Questions & Answers
QUESTION:
A uniform spherical shell of mass M = 4.5 kg and radius R = 8.5 cm can rotate about a vertical axis on frictionless bearings (Fig. 10-47). A massless cord passes around the equator of the shell, over a pulley of rotational inertia \(I=3.0 \times 10^{-3} \mathrm{~kg} \cdot \mathrm{m}^{2}\) and radius r = 5.0 cm, and is attached to a small object of mass m = 0.60 kg. There is no friction on the pulleys axle; the cord does not slip on the pulley. What is the speed of the object when it has fallen 82 cm after being released from rest? Use energy considerations.
ANSWER:Step 1 of 4
We need to find the velocity of the mass m = 0.6 kg when it is released from rest and had fallen to a length of h = 0.82 m. The mass is connected to a pulley by a string which passes around a uniform spherical shell of mass M = 4.5 kg and radius R = 0.085 m.
Given:
Mass of the sphere: \(M=4.5 \mathrm{~kg}\)
Mass of the object: \(m=0.6 \mathrm{~kg}\)
Radius of the pulley: \(r=0.05 \mathrm{~m}\)
Moment of Inertia of the pulley: \(I_{\text {Pulley }}=3 \times 10^{-3} \mathrm{kgm}^{2}\)