Physics

posted by Joe

A bowling ball rolls without slipping up a ramp that slopes upward at an angle (beta) to the horizontal. Treat the ball as a uniform, solid sphere, ignoring the finger holes.

What is the acceleration of the center of mass of the ball?
Express your answer in terms of the variable (beta) and appropriate constants.(this was g*sin(beta)/1.4)

What minimum coefficient of static friction is needed to prevent slipping?
Express your answer in terms of the variable (beta) and appropriate constants.

The second part I don't understand how to do. Help is appreciated :/

1. drwls

The equation of motion for a solid sphere rolling uphill is
M*g sinbeta-(2/5)M*a = M*a
The second term on the right is the friction force, assuming no slipping.
Rearranging gives you
a = g*sinbeta/1.4

To prevent slipping, the friction force
(2/5)M*a = (2/5)M*g*sinbeta*(5/7)
= (2/7)*M*g*sinbeta must be less than the maximum static friction force
M*g*cosbeta*Us.
Us is the static friction coefficientr.

Slipping starts when the terms on both sides are equal, in which case
Us = (2/7)*tanbeta

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