Question # Two adults and a child want to push a wheeled cart in thedirection marked x in Fig. 4.29 The two adults push with horizontalforces F_{1} and F_{2} as

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ANSWERED Two adults and a child want to push a wheeled cart in thedirection marked x in Fig. 4.29 The two adults push with horizontalforces $$\displaystyle{F}_{{{1}}}{\quad\text{and}\quad}{F}_{{{2}}}$$ as shown in the figure. (a)Find the magnitude and direction of the smallest force that thechild should exerts the minimum force found in part (a), the cartaccelerates at 2.0 $$\displaystyle\frac{{m}}{{s}^{{{2}}}}$$ in the +x direction. What is theweight of the cart? a) The resultant must have no y-component, and sothe child must push with a force withy-component $$\displaystyle{140}{\sin{{\left({30}\right)}}}-{100}{\sin{{\left({60}\right)}}}={16.6}{N}$$. For the child to exert the smallestpossible force, that force will have no x-component, so thesmallest possible force has magnitude 16.6 N and is at an angle of 270, or 90 clockwise from the +xdirection.
b) $$\displaystyle\sum{F}={m}{a}$$
$$\displaystyle{m}={\frac{{\sum{F}}}{{{a}}}}={\frac{{{140}{\sin{{\left({30}\right)}}}+{100}{\sin{{\left({60}\right)}}}}}{{{2}}}}={85.6}{k}{g}$$
$$\displaystyle{w}={m}{g}={\left({85.6}\right)}{\left({9.8}\right)}={840}{N}$$