Tangential force acting on a skier has been set to zero?

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The discussion centers on the tangential force acting on a skier on a smooth, curved slope, questioning why the sum of tangential forces (Ft) is set to zero. Participants highlight that while friction is absent, neglecting the weight component along the slope raises concerns, especially since the slope is curved and the angle (theta) changes continuously. The conversation also touches on the implications of the slope's shape, specifically a parabolic curve, and how this affects the skier's motion at point A. The slope at point A is identified as zero, leading to inquiries about the weight component at that specific point. Overall, the discussion emphasizes the complexities of analyzing forces on a skier navigating a curved slope.
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Can anyone explain why sum of Ft has been set to be = 0? The slope is smooth so no frictional forces act but by setting it to 0 they are neglecting the component of the weight along the slope? Having said that, this is a curved slope and not a straight one so does the component of the weight along the direction of motion vary continuously (since theta varies?)
 
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If it's a parabola what is the slope at point A ?
 
CWatters said:
If it's a parabola what is the slope at point A ?
It's 0?
 
So what is the "component of weight along the slope" at point A?
 
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