ball. In Figure 11.36, a ball of mass M and radius R rolls smoothy from rest dow

Question

ball. In Figure 11.36, a ball of mass M and radius R rolls smoothy from rest down a ramp onto a circular loop of radius 0.46 m. The initial height of the ball is h = 0.37 m. At the loop bottom, the magnitude of the normal force on the ball is 1.98 Mg. The ball consists of an spherical shell (of a certain uniform density) that is glued to a central sphere (of a different uniform density). The rotational inertia of the ball can be expressed in the general form t = beta MR2, but beta is not 0.4 as it is for a ball of uniform density. Determine beta.

Explanation / Answer

suppose at bottom ball have a speed of v.

then , N = mg + mv2 /0.46 = 1.98mg

v2 /0.46 = 9.604

v = 2.1 m/s

now using energy cosnervation ,

mgh = mv2 /2 + I2 /2        and = v/R

mg x 0.37 = m x 2.12 /2   + mR2 x 2.12 /R

3.626 - 2.205   = x 4.41

= 0.3222

Related Questions

Navigate

• Browse (All)
• Browse B
• Subjects

---

---

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