A block is projected up a rough inclined plane. It initially goes up, then comes back to the initial point. If time of ascent is and time of descent is . Then which of the following is correct?
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The derivations for t a and t d are fairly straightforward. Some key points are that the gravity and friction forces add (relative to each other) on the way up and subtract on the way down. The travel distances are the same both ways. On the way down, the particle starts with no speed (unlike the upward case), but has a net force accelerating it rather than retarding it. The results are:
t a = g s i n θ + μ g c o s θ v 0
t d = ( g s i n θ + μ g c o s θ ) ( g s i n θ − μ g c o s θ ) v 0
By inspection, t d will generally be larger than t a