Example $(10$ points$)$ A thin beam with mass $M$ lies on two wheels, each of which with mass $m$ and radius $R.$ The spokes of the wheels are without mass. Due to its deadload the systems moves down the inclined plane. No slip is assumed between the wheels and the inclined plane as well as the beam. The movement of the syatem is described by the coordinate $x(t).$

Given:

$R=0,6m,g=9,81m{s}^{-2},m=1,7kg,$

$M=4,8kg,=34,$

Insert the correct solution at an accurracy of four significant numbers into the corresponding fields:

a$)$ Evaluate the magnitudes of the d'Alemert forces $|F_{H1}|$ und $|F_{H2}|$ of the wheels dependent on $x^{}.(2$ points$)$

$|F_{H1}|=|F_{H_2}|,x^{}[(kg)(m)s^{-2}]$

b$)$ Evaluate the magnitudes of the d'Alemert moments $|M_{H_1}|$ und $|M_{H_2}|$ of the wheels dependent on $x^{}.(6$ points$)$

$|M_{H1}|=|M_{H_2}|,x^{}[(kg)m^2{s}^{-2}]$

c$)$ Evaluate the magnitudes of the d'Alemert forces $|F_{HB}|$ des Balkens in Abh$$ngigkeit von $\stackrel{}{x}.(2$ points$)$

$|F_{HB}|=,x^{}[(kg)(m)s^{-2}]$

d$)$ Evaluate the acceleration of the beam $\stackrel{}{x}$ using the principle of virtual work. $(2$ points$)$

$x^{}$

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