A uniform spherical shell of mass M = 6.00 kg and radius R = 0.640 m can rotate

Question

A uniform spherical shell of mass M = 6.00 kg and radius R = 0.640 m can rotate 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 = 0.0650 kg·m2 and radius r = 0.120 m, and is attached to a small object of mass m = 2.60 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 when it has fallen a distance 0.513 m after being released from rest? Use energy considerations.

Explanation / Answer

Let the speed = V

Using conservation of energy ::

Potential energy of object = Rotational KE of sphere + Rotational KE of pulley + K.E of the object

mgh = (0.5) (2/3 MR2) (V/R)2 + (0.5) I (V/r)2 + (0.5) m V2

(2.60) (9.8) (0.513) = (0.5) (2/3 (6) V2 + (0.5) (0.065) (V/0.12)2 + (0.5) (2.60) V2

V = 1.86 m/s

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.