The motion of a bead on a sinusoidal track. Very tricky and dense, thanks in advance!

by aak452
Tags: bead, motion, parametric, sinusoidal, velocity
aak452 is offline
Oct26-11, 04:42 PM
P: 1
1. The problem statement, all variables and given/known data

a If the bead starts at the origin at time t=0, how long does it take for it to reach the
end of the track (30m away in the figure)? Provide the answer in terms of v[itex]_{}[/itex]. b How does the parameter α depend on time, ie. what is α(t)?
d What is the velocity vector as a function of t (in symbolic form)?
e What is the acceleration vector as a function of t (in symbolic form)?
f Based on your results for the velocity and acceleration, what is the radius of the "kissing circle" at the top of the track? Recall, the kissing circle at a given point goes through the point, has the same tangent as the curve, and a radius that reproduces the perpendicular component of the acceleration, i.e.:
R = |→v|^2/a?
f Will Rbottom the radius of the kissing circle at the bottom of the track
be <, > or = to R[itex]_{}[/itex]?
h How fast would the rod need to move for the bead to leave the track? Provide an answer in symbolic form and a numerical value for the speed.

3. The attempt at a solution
a) I tried approximating the length of the track through simply turning each curve into a line. Then divide the total distance by v[itex]_{}[/itex]?
b)α is just the x-position of the bead, so it would increase depending on time. This answer, however, seems WAY too simple...perhaps I am interpreting the question wrong?
c) I tried taking the derivative of the given parametric equation...but am not sure how to derive a parametric equation, as it has two parts.
d)I suppose I would the derive the equation obtained from deriving the original parametric equation?
After this point, I am just hopelessly lost. I think I am having trouble applying the easy concepts I learn from the textbook to more conceptual problems. Any help would be MUCH appreciated!
1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution
Phys.Org News Partner Science news on
Simplicity is key to co-operative robots
Chemical vapor deposition used to grow atomic layer materials on top of each other
Earliest ancestor of land herbivores discovered

Register to reply

Related Discussions
Tricky Track Brain Teasers 10
Bead on a Wire and Harmonic Motion Introductory Physics Homework 1
A bead in circular motion in space! Introductory Physics Homework 1
tricky track problem (continued) Introductory Physics Homework 1
tricky track/friction problem (again) Introductory Physics Homework 2