Nonuniform ball. In the figure below, a ball of mass M and radius R rolls smooth

Question

Nonuniform ball. In the figure below, a ball of massMand radiusRrolls smoothly from rest down a ramp and onto a circular loop of radius0.53m. The initial height of the ball ish=0.32m. At the loop bottom, the magnitude of the normal force on the ball is 2.00Mg. The ball consists of an outer spherical shell (of a certain uniform density) that is glued to a central solid sphere (of a different uniform density). The rotational inertia of the ball can be expressed in the general formI=?MR2, but?is not 0.4 as for a ball with a single uniform density. Determine?.

Explanation / Answer

velocity at bottom = mv^2/r=2mg

=>v=3.223 m/s

now energy conservation

mgh=0.5*m*v^2 +0.5*?mr^2* v^2/ r^2

=>9.8*0.32=0.5*3.223*(1+ ? )

=>1.946=1+ ?

=> ?= 0. 946

Related Questions

Navigate

• Browse (All)
• Browse N
• Subjects

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