Friday

March 27, 2015

March 27, 2015

Posted by **Karla** on Tuesday, March 27, 2007 at 12:08pm.

You will find the moment of inertia (I) of a hollow sphere of radius R derived here: (Broken Link Removed)

I = (2/3) MR^2

If it rolls wthout slippng, the increase in Kinetic Energy equals the decrease in Potential Energy. The kinetic energy is in two parts, rotation and translation.

M g H sin 38 = (1/2) M V^2 + (1/2) I (V/R)^2

= [(1/2) + (1/3)] M V^2

The M's and R's cancel and

gH sin 38 = (5/6) V^2

V = sqrt (1.2 g H sin 38) = sqrt (2 a H)

where a is the acceleration

a = 0.6 g sin 38

Use that acceleration and Newton's second law t compute the actual friction force, F.

M g sin 38 - F = M a

Mg sin 38 - M*0.6 g sin 38 = F

F = 0.4 M g sin 38

To provide this amount of friction, the static coefficient of friction mu,s must equal or exceed a value given by

M g cos 38 * mu,s = 0.4 M g sin 38

mu,s - 0.4 tan 38

Higher values of mu,s will also prevent slipping

The V/R term is the angular rtation velocity.

- xcqd kxuhc -
**xcqd kxuhc**, Sunday, February 1, 2009 at 7:38amwabv eqjd ncok cnwytrg kdovzwpnl yqbhix xtjhf

**Answer this Question**

**Related Questions**

Physics - A hollow spherical shell with mass 2.45kg rolls without slipping down ...

Physics - A hollow spherical shell with mass 2.45kg rolls without slipping down ...

Physics - A hollow spherical shell with mass 2.45kg rolls without slipping down ...

Physics Classical Mechanics - A hollow cylinder of outer radius R and mass M ...

Physics - A 190 g basketball has a 37.3 cm diameter and may be approximated as a...

Physics - A solid sphere of uniform density starts from rest and rolls without ...

Physics - A bowling ball rolls without slipping up a ramp that slopes upward at ...

Physics - A box of textbooks of mass 25.3 kg rests on a loading ramp that makes ...

Physics - A uniform, spherical bowling ball of mass m and radius R is projected ...

physics - You are skiing and have a mass of 47 kg and are on a slope making an ...