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

V = volume = 4/3(pi)R

(Rho) = M/V

I

dm = (Rho)*dV

ME = K

L=I

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.

I know that f

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.

It would just be 7/10*M*v

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 m

µ

Experts Exchange Solution brought to you by

Enjoy your complimentary solution view.

Get every solution instantly with Premium.
Start your 7-day free trial.

I wear a lot of hats...

"The solutions and answers provided on Experts Exchange have been extremely helpful to me over the last few years. I wear a lot of hats - Developer, Database Administrator, Help Desk, etc., so I know a lot of things but not a lot about one thing. Experts Exchange gives me answers from people who do know a lot about one thing, in a easy to use platform." -Todd S.

Experts Exchange Solution brought to you by

Your issues matter to us.

Facing a tech roadblock? Get the help and guidance you need from experienced professionals who care. Ask your question anytime, anywhere, with no hassle.

Start your 7-day free trialHere 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.

Math / Science

From novice to tech pro — start learning today.

Experts Exchange Solution brought to you by

Enjoy your complimentary solution view.

Get every solution instantly with Premium.
Start your 7-day free trial.

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.