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Problem 7.27

7.27.

The initial potential energy of the block is mgh. The incline does work on the block in the form of friction. Conservation of energy gives us

tex2html_wrap_inline376

Since the block starts and ends at rest, tex2html_wrap_inline378 . The work done by friction is given by

tex2html_wrap_inline380 where we have used the fact that the normal force is given by tex2html_wrap_inline382 . Then the distance d is given by

tex2html_wrap_inline386

pullling it all together we find that

tex2html_wrap_inline388

tex2html_wrap_inline390

Solving for tex2html_wrap_inline392 yields the desired result.

tex2html_wrap_inline394



Jason George Zeibel
Thu Oct 30 00:58:31 EST 1997