Homework H4.F - Fa22

Problem statement
Solution video

DISCUSSION THREAD

Any questions??


As P moves around on the circular track, two things occur:

  1. The normal force N on P due to the circular guide is proportional to the centripetal acceleration  of P: N = mv2/R.
  2. A friction force opposes its motion, where the sliding friction force is proportional to the normal force between the circular guide and P: f = μkN = mμkv2/R.
  3. From this, we see that the friction force goes to zero as the speed goes to zero. What does this imply about P coming to rest? Can you see this in the animation of the motion below?

 

HINTS:
You will need to use the chain rule of differentiation to set up this problem: dv/dt = (dv/ds)(ds/dt) = v (dv/ds).

One thought on “Homework H4.F - Fa22”

  1. After doing the integration, I found that the speed decays exponentially as a function of distance s (which makes sense). I rearranged for v in terms of s and took a limit as v goes to 0 and found that the particle travels an infinite distance. It seems like this might be possible since the friction force drops to zero as the particle keeps moving, so the speed never drops to zero, but that explanation alone isn't sufficient, since I can't tell whether the distance traveled diverges or converges even though the particle keeps moving forever. Is there a good way to confirm this result mathematically (an improper integral maybe?) or did I make a mistake? Thanks.

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