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&nbsp;F1&nbsp;and&nbsp;F2&nbsp;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&nbsp;ms2&nbsp;in the +x direction. What is theweight of the cart?

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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&amp;nbsp;F1&amp;nbsp;and&amp;nbsp;F2&amp;nbsp;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&amp;nbsp;ms2&amp;nbsp;in the +x direction. What is theweight of the cart?

Theodore Schwartz · Accepted Answer

a) The resultant must have no y-component, and sothe child must push with a force withy-component 140sin⁡(30)−100sin⁡(60)=16.6N. 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) ∑F=ma  m=∑Fa=140sin⁡(30)+100sin⁡(60)2=85.6kg  w=mg=(85.6)(9.8)=840N

Jeffrey Jordon · Accepted Answer

a)Forces in the +y-direction:  F1y=100sin⁡60∘=10032=86.6N  F2y=−140sin⁡30∘=−1402=−70N  So, the smallest force that the child should exert:  F=86.6−70=16.6N at 90∘ from +x clockwise (-y-direction).  b)Result forces in the +x-direction:  Fx=F1x+F2x=100cos⁡60∘+140cos⁡30∘=1002+14032=171.24N  The weight of the cart:  m=Fxa=171.242=85.62kg

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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