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Eclair_de_XII

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## Homework Statement

"Figure 9-44 shows an arrangement with an air track, in which a cart is connected by a cord to a hanging block. The cart has mass ##m_1=\frac{3}{5}kg##, and its center is initially at

*xy*coordinates ##(-\frac{1}{2}m,0)##; the block has mass ##m_2=\frac{2}{5}kg##, and its center is initially at

*xy*coordinates ##(0,-\frac{1}{10}m)##. The mass of the cord and pulley are negligible. The cart is released from rest, and both cart and block move until the cart hits the pulley. The friction between the cart and the air track and between the pulley and its axle is negligible. (a) In unit-vector notation, what is the acceleration of the center of mass of the cart-block system? (b) What is the velocity of the com as a function of time ##t##?

## Homework Equations

##m_1=\frac{3}{5}kg##

##s_1=<-\frac{1}{2}m,0>##

##m_2=\frac{2}{5}kg##

##s_2=<0,-\frac{1}{10}m>##

##s_{com}=<\frac{Σmx}{Σm},\frac{Σmy}{Σm}>##

##F_{pulley-system}=(m_2-m_1)g=(m_1+m_2)a##

##a_{pulley-system}=\frac{(m_2-m_1)g}{(m_1+m_2)}##

## The Attempt at a Solution

##x_{com}=\frac{(\frac{3}{5}kg)(-\frac{1}{2}m)}{1kg}=-\frac{3}{10}m##

##y_{com}=\frac{(\frac{2}{5}kg)(-\frac{1}{10}m)}{1kg}=-\frac{1}{25}m##

##s_{com}=<-\frac{3}{10}m,-\frac{1}{25}m>##

##a_y=(g)(\frac{m_2-m_1}{m_2})=(\frac{5}{2}kg^{-1})(\frac{49}{5}\frac{m}{s^2})(\frac{2}{5}kg-\frac{3}{5}kg)=-\frac{49}{10}\frac{m}{s^2}##

##a_x=(g)(\frac{m_1-m_2}{m_1})=(\frac{5}{3}kg^{-1})(\frac{49}{5}\frac{m}{s^2})(\frac{3}{5}kg-\frac{2}{5}kg)=\frac{49}{15}\frac{m}{s^2}##

I don't really know how to do this problem properly.

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