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\begin{document}

\frame{\frametitle{\b Work and Energy II-1} \bigskip

{\bf Kinetic Energy (1):} 
$$ E_k^{\rm final}  = E_k^{\rm initial} + Work\,.$$
% \bigskip

{\bf Hydro Electric Plant (2):} 
$$ W = m\,g\,h\,,~~~{\rm kWh} = 1000\times 3600\,J.$$
% \bigskip

{\bf Block Sliding into Spring (3):} Energy conservation!
$$ W= m\,g\,h = \frac{1}{2}\,k\,x^2\,. $$
% \bigskip

{\bf Toy Sled (4):} Energy conservation again. Then
$$ \triangle v = \mu_k\,g\,\triangle t\,,
   ~~~~x = v_{\rm average}\,t\,. $$
\vskip 20pt }

\frame{\frametitle{\b Work and Energy II-2} \bigskip

{\bf Two Segments Ramp (5):}  
$$ \sin(\alpha) = \frac{h/2}{L_1}\,,~~~
   \sin(\theta) = \frac{h/2}{L_2}\,,~~~
   W_i = m\,g\,\mu_k\,L_i\,\cos({\rm angle}_i)\,~~(i=1,2)\,. $$ 
% \bigskip

{\bf Vertical Spring (6):} Again, use energy conservation! \bigskip

{\bf Curved Bowl (7):} 
$$ m\,g\,h_{\rm min} = F_{\mu}\,L\,.    $$
\vskip 20pt }

\end{document}
