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\begin{document}

\frame{\frametitle{\b Newton's Laws III-1 } \bigskip

{\bf Mass suspended inside accelerating van (1):} 

$$ F_x = m\,a\,,~~F_y = m\,g\,,~~\tan(\theta) = \frac{Fx}{F_y}\,,
   ~~F = \sqrt{F_x^2+F_y^2}\,.\ $$
% \bigskip

{\bf Boxes (2):}  
$$ F = m\,g\,\sin(\theta)\,.$$
% \bigskip

{\bf Inlcined plane (3):}
$$ \sin(\theta) = \frac{a}{g}\,. $$

{\bf Pulley (4).}

Acceleration:
$$ F = |m_2-m_1|\,g\,,~~a = \frac{F}{M}\,. $$
Tension:       
$$ T = {\rm mass?}\ (a+g)\,.                   $$
\vskip 20pt }

\frame{\frametitle{\b Newton's Laws III-2 } \bigskip

{\bf Circular motion (5).} % \bigskip

Maximum speed:
$$ F_{\max} = M\,\frac{v_{max}^2}{R}\,.$$
Tension on top:
$$ T = M\,(a-g)\,,~~a=?\,.$$

{\bf Conical pendulum (6).} % \bigskip

Complete revolution:
$$ a_x = \frac{v^2}{R}\,,~~\tan(\theta) = \frac{a_x}{g}\,,
   ~~T = \frac{2\pi\,R}{v}\,.$$

Tension:
$$ T = \sqrt{T_x^2+T_y^2}\,.$$

{\bf Cicular motion (7):} Pail of water.% \bigskip
$$ g = \frac{v^2}{R}\,.     $$
\vskip 20pt }

\end{document}
