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May 6, 2016

# Homework Help: Physics

Posted by Helen on Sunday, December 4, 2011 at 1:43am.

A bowling ball of mass M and radius R is thrown along a level surface so that initially ( t= 0) it slides with a linear speed but does not rotate, see the figure. As it slides, it begins to spin, and eventually rolls without slipping.

How far has the ball moved down the lane when it starts rolling without slipping?

What are its final linear speed?

What are its final rotational speed?

Thanks:]
• Physics - drwls, Sunday, December 4, 2011 at 2:15am

You need to specify kinetic friction coefficient and the initial velocity.

• Physics - Helen, Sunday, December 4, 2011 at 2:23am

it says to answer it in terms of those coefficients

• Physics - Helen, Sunday, December 4, 2011 at 2:25am

• Physics - Damon, Sunday, December 4, 2011 at 4:39am

Initial w, angular velocity, is zero.
now while sliding
torque = I alpha
mu m g r = (2/5) m r^2 alpha
alpha = (5/2) mu g / r
and
F = m a
mu m g = m a
a = mu g
w = alpha t
v = Vi - a t
when does w r equal v (no slip)
r alpha t = v = Vi - a t
(5/2) mu g t = Vi - mu g t
(7/2)mu g t = Vi
so
t = (2/7)Vi/(mu g)
that is the time sliding
work back up to get distance and final v

Check that with energy argument:
frictional work done = mu m g d

Initial Ke - frictional work = Final Ke
(1/2) m Vi^2 - mu m g d = (1/2) m v^2 +(1/2) (2/5) m r^2 (v^2/r^2)

Vi^2 - 2 mu g d = (7/5)v^2