Question

# Bowling Ball. A bowling ball rolls without slipping up a ramp that slopes upward at an...

Bowling Ball. A bowling ball rolls without slipping up a ramp that slopes upward at an angle to the horizontal. Treat the ball as a uniform solid sphere of mass M and radius R, ignoring the finger holes.

a) Draw the free-body diagram for the ball. Explain why the friction force must be directed up the ramp.

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?

b) Fr=I(a/r)
I=2/5mr^2
F=2/5ma

mg*sinb-f=ma
mg*sinb-2/5ma=ma
g*sinb=7/5a
a=5/7g*sinb(use negative sign if direction is also needed)

Note: b is the angle

c)
mg*sinb-(us)mg*cosb=m*5/7g*sinb
(us)*cosb=2/7*sinb
us=2/7*tanb

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