   Chapter 8, Problem 52P

Chapter
Section
Textbook Problem

A 240-N sphere 0.20 m in radius rolls without slipping 6.0 m down a ramp that is inclined at 37° with the horizontal. What is the angular speed of the sphere at the bottom of the slope if it starts from rest?

To determine
The angular speed of the sphere at the bottom of the slope if it starts from rest.

Explanation

Given info: The weight of the sphere is 240N , radius of the sphere is 0.20m , length of the slope is 6.0m , the angle of the ramp is 37° , and acceleration due to gravity is 9.8m/s2 .

Explanation: The conservation of mechanical energy of the system is used for the angular speed of the sphere that is KEr,f+KEt,f+PEg,f=KEr,i+KEt,i+PEg,i but initially, the translational and rotational kinetic energies are zero. At the bottom of the slope, the potential energy would be zero. Now the conservation of mechanical energy is written as 12Iωf2+12mvt2+0=0+0+mglsinθ and the moment of inertia of the sphere is I=2mr2/3 .

The formula for the angular speed of the sphere at the bottom of the slope if it starts from rest is,

ωf=107glsinθr2

• g is acceleration due to gravity

Still sussing out bartleby?

Check out a sample textbook solution.

See a sample solution

The Solution to Your Study Problems

Bartleby provides explanations to thousands of textbook problems written by our experts, many with advanced degrees!

Get Started 