Solved

Friction, Kinetic Energy, & Momentum of a Sphere down an inclined plane

Posted on 2012-04-08
7
59 Views
Last Modified: 2016-06-25
1. The problem statement, all variables and given/known data

A solid sphere of mass 3.00 kg and radius 12.5cm rolls without slipping down an incline of
angle 13.5 degree for 250 m. Find the minimum coefficient of static friction required for a
rolling without slipping. What is the velocity of the center of the sphere at the bottom of the
incline? What is the angular momentum at that point? That is the kinetic energy at this point? Make a drawing, show the forces and torques. Indicate the torque which you are using for your calculations. Derive your formulas.

[Figures can all be rounded to 3 sig figs.]

M = 3.00 kg
R = 12.5 cm = 0.123 m
theta = 13.5
d = 250 m
h = d*sin(theta) = 58.4 m

2. Relevant equations

V = volume = 4/3(pi)R3; dV/dR = 4(pi)R2
(Rho) = M/V
Icm = (integral)r2dm
dm = (Rho)*dV
ME = Krot + Kcm - U
L=Ia(omega); Ia = Icm + Md^2 where d is the distance between the two axes

3. The attempt at a solution

Progress on problem
I found the velocity fine, and the answer matched with the solutions, but I can't seem to get  the angular momentum, coefficient of friction, or the kinetic energy at the bottom.

For friction...
I know that fs = µs*N & N = Mgcos(theta) but how do I find out what fs is?

For angular momentum...
I started with the L equation above, then subbed in the values from my previously derived work (see image) but the answer I got was way off from the correct answer.

For kinetic energy at the bottom...
It would just be 7/10*M*v2 minus the work done by friction correct? So if I can somehow find the work done by friction over the distance traveled, then I find the amount of kinetic energy left at the bottom... would that be right?

I know there are a lot of questions here, but since they're all related to the same problem, I thought I would take a shot and just put all the thoughts in my head about this problem and just have the community pick at what they feel they want to attack first, and maybe help me make a game plan for this sort of problem. Thanks in advance for any help given!



Official Answers:
V=28.6 m/s
L=4.39 kg m2/s
µs=0.0686
0
Comment
Question by:Zenoture
  • 4
7 Comments
 
LVL 27

Accepted Solution

by:
d-glitch earned 250 total points
Comment Utility
The sphere rolls without slipping, so the kinetic energy at every point is the sum of center-of-mass kinetic energy and the rotational kinetic energy.
All the work done by friction goes into rotational kinetic energy.  No sliding implies no heat loss.

Note that the ramp is long and shallow.  Not at all like your drawing.
0
 
LVL 27

Assisted Solution

by:aburr
aburr earned 250 total points
Comment Utility
d-glitch has asked a number of good questions which will help you to get the right answers.
Here is another related.
Just what is the amount of work done by friction? In this case the answer can be stated immediately which no calculations.
0
 
LVL 27

Expert Comment

by:aburr
Comment Utility
Both answers gave a hint of the type permitted by he homework rules and should be awarded points
0
 
LVL 27

Expert Comment

by:aburr
Comment Utility
Both answers gave help as permitted by the homework rules
0
 
LVL 27

Expert Comment

by:aburr
Comment Utility
See previous comment
0

Featured Post

What Security Threats Are You Missing?

Enhance your security with threat intelligence from the web. Get trending threat insights on hackers, exploits, and suspicious IP addresses delivered to your inbox with our free Cyber Daily.

Join & Write a Comment

Suggested Solutions

Title # Comments Views Activity
derivative 19 23
springs 9 250
Loan to Value to interest rate relationship formula 1 147
Geomentry-Fundamental concepts-Angles 3 53
Complex Numbers are funny things.  Many people have a basic understanding of them, some a more advanced.  The confusion usually arises when that pesky i (or j for Electrical Engineers) appears and understanding the meaning of a square root of a nega…
Lithium-ion batteries area cornerstone of today's portable electronic devices, and even though they are relied upon heavily, their chemistry and origin are not of common knowledge. This article is about a device on which every smartphone, laptop, an…
In this tutorial you'll learn about bandwidth monitoring with flows and packet sniffing with our network monitoring solution PRTG Network Monitor (https://www.paessler.com/prtg). If you're interested in additional methods for monitoring bandwidt…
When you create an app prototype with Adobe XD, you can insert system screens -- sharing or Control Center, for example -- with just a few clicks. This video shows you how. You can take the full course on Experts Exchange at http://bit.ly/XDcourse.

744 members asked questions and received personalized solutions in the past 7 days.

Join the community of 500,000 technology professionals and ask your questions.

Join & Ask a Question

Need Help in Real-Time?

Connect with top rated Experts

10 Experts available now in Live!

Get 1:1 Help Now