Question

A block is projected at an incline at angle θ. It returns to its initial position with half of its initial speed. Show that the coefficient of kinetic friction is Uk= 3/5 tanθ

Answer 1

\[KE _{i} = PE _{f} +W _{f}\]
\[KE _{f} = PE _{f} -W _{f}\]
\[\frac{ KE _{i} = PE _{f} +W _{f} }{KE _{f} = PE _{f} -W _{f}} -> 4= \frac{PE _{f} +W _{f} }{ PE _{f} -W _{f} }\]
\[4 (PE _{f} -W _{f} )=PE _{f} +W _{f} \]
\[3PE _{f} =5W _{f} \]
\[\frac{ 3 }{5 } PE _{f} =W _{f}\]

Answer 2

\[PE = mgd \sin \theta \]
and
\[W _{f} = \mu mg \cos \theta *d\]

Answer 3

all good?

Answer 4

those were unfortunate choices I made on the subscripts... the 'i' on 'KEi' is for initial
the 'f' on 'KEf' and 'PEf' is for final
and the 'f' on 'Work' is to indicate work due to friction...