Acceleration of a rolling sphere up a ramp

[pathmaker]

Homework Statement

"A bowling ball rolls without slipping up a ramp that sloped upward at an angle B to the horizontal. Treat the ball as a uniform, sold spehere, ignoring the finger holes. a) explain why the friction force must be directed uphill. b) what is the acceleration of the center of mass of the ball? c) what minimum coefficient of static friction is needed to prevent slipping?

Homework Equations

I=2/5mr^2
F=ma, torque=fr=I alpha, a=r alpha
f=mu n

The Attempt at a Solution

b) f-mgsinB=ma
fR=Iaplhpa
fR=I(a/r)
f=2/5ma
2/5ma-mgsinB=ma
a=-5/3gsinB

c)f=2/5m(-5/3gsinB)
f= -2/3mgsinB
f/n=mu
mu>-2/3tanB
??

 

[Doc Al]

b) f-mgsinB=ma
fR=Iaplhpa
fR=I(a/r)
f=2/5ma
2/5ma-mgsinB=ma
a=-5/3gsinB

Careful with signs: The acceleration is down the incline.

 

[pathmaker]

so a = 5/7gsinB
is that the same as it the ball was moving down the ramp?

 

[Doc Al]

Yep.

 

[pathmaker]

thanks