April 18, 2014

Homework Help: Physics

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

A hollow, spherical shell with mass 2.00 kg rolls without slipping down a slope angled at 38.0 degrees. (a) Find the acceleration, the friction force, and the minimum coefficient of fricition needed to prevent slipping.

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.

Answer this Question

First Name:
School Subject:

Related Questions

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 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 - A solid sphere of uniform density starts from rest and rolls without ...
physics - A thin spherical shell of mass M = 2.00 kg is released from rest at ...
Physics - A box with a mass of 7.00 kg is at rest on a ramp that is at an angle ...
physics - A spherical bowling ball with mass m = 4.1 kg and radius R = 0.116 m ...
physics - solid sphere of uniform density starts from rest and rolls without ...
Physics - A 1-kg thin hoop with a 50-cm radius rolls down a 47 slope without ...