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

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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.