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LucidLunatic
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Homework Statement
Inscribe N chords of equal length within a circle of radius r. A body of mass m travels at constant speed v along the chords and is perfectly reflected in each collision with the circle (there is no momentum change tangent to the circle). Show that the radial momentum change per collision is Δp =mvsinθ, where θ is the angle between tangent and chord.
Homework Equations
Δpr = pr1-pr0
The Attempt at a Solution
We can write
p0 = mvsinθ \hat{r} + mvcosθ\hat{\theta}
p1 = -mvsinθ \hat{r} + mvcosθ\hat{\theta}
therefore Δp = -2mvsinθ.
This seems like a fairly simple problem, so I'm not sure where I'm going wrong. The later steps of this problem then show that the net centripetal force obeys F = mv^2/r as N→∞, but that depends on getting the correct answer here. What am I missing? Note: this is me going through problems in a book, not an actual homework assignment.