How come the y component is not negative since it’s pointing down? Thank you. Ca

Question

How come the y component is not negative since it’s pointing down? Thank you. Calculate the deceleration of a snow boarder going up a 5.0 slope assuming the coefficient of friction for waxed wood on wet snow. The result of Exercise 5.9 may be useful, but be careful to consider the fact that the snow boarder is going uphill. Explicitly show how you follow the steps in Problem-Solving Strategies. 10. Solution Using the free body diagram: net F. _ w, + f-ma and net Fy = N-wy = 0 where w,-mg . Given ?-5° and 14-0.100 (from Table 5.1). Find: a. Using trigonometry gives wx-wsin ?. Also, we know f-MN so that f-umg cose. Solving for a gives: a-w,+/-(mgsin ? + u mg cos e)-g(sin0+mcosB so that a-(9.80 mis%ìn5° + (0.100)cos")-1.83 m/s2

Explanation / Answer

While writing Newton's 2nd Law, i.e. Net Force = Mass x acceleration

since acceleration is in the direction of net force, therefore mgSin 5 is taken as positive when it is in the direction of acceleration, and it is taken as negative, when it is opposite to the direction of acceleration.

In the question given, object is retarding, that means acceleration is downward, and hence mgSin 5 is taken as positive.

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