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

\[PE = mg*d \sin \theta \]
\[W _{f} =\mu _{k} *mg* \cos \theta * d\]
\[KE _{1} = PE +W _{f}\]
\[KE _{2} = PE - W _{f}\]
\[\frac{ KE _{1}}{ KE _{2}} = 4 = \frac{PE + W _{f} }{PE - W _{f} }\]
\[ 4 (PE - W _{f} )= PE + W _{f} \]
\[\frac{ 3 }{ 5 } PE = W _{f} \]
\[\frac{ 3 }{ 5 } mg∗dsinθ =μk∗mg∗\cosθ∗d\]