A uniform spherical shell of mass M = 11.0 kg and radius R = 0.480 m can rotate

Question

A uniform spherical shell of mass M = 11.0 kg and radius R = 0.480 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 = 0.160 kg m2 and radius r = 0.110 m, and is attached to a small object of mass m = 1.60 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 0.700 m after being released from rest? Use energy considerations.

Explanation / Answer

the law of conservation of energy:

m g h = 0.5 (m v^2 + 0.5 I w^2 + 0.5 I' w'^2)

m g h = 0.5 (m v^2 + I (v^2/r^2) + I' (v^2/R^2))

m g h = 0.5 (m + I/r^2 + (2/3MR^2)/R^2) v^2

m g h = 0.5 (m + I/r^2 + 2M/3) v^2

1.60*9.8*0.7 = 0.5*(1.60 + 0.16/0.11/0.11 + 2*11/3) v^2

v = 0.995 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.